Greek Science

There is considerable agreement that Thales was born in Miletus in Greek Ionia in the mid 620s BCE and died in about 546 BCE, but even those dates are indefinite. Aristotle, the major source for Thales's philosophy and science, identified Thales as the first person to investigate the basic principles, the question of the originating substances of matter and, therefore, as the founder of the school of natural philosophy. Thales was interested in almost everything, investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics. He proposed theories to explain many of the events of nature, the primary substance, the support of the earth, and the cause of change. Thales was much involved in the problems of astronomy and provided a number of explanations of cosmological events which traditionally involved supernatural entities. His questioning approach to the understanding of heavenly phenomena was the beginning of Greek astronomy. Thales's hypotheses were new and bold, and in freeing phenomena from godly intervention, he paved the way towards scientific endeavour. He founded the Milesian school of natural philosophy, developed the scientific method, and initiated the first western enlightenment. A number of anecdotes is closely connected to Thales's investigations of the cosmos. When considered in association with his hypotheses they take on added meaning and are most enlightening. Thales was highly esteemed in ancient times, and a letter cited by Diogenes Laertius, and purporting to be from Anaximenes to Pythagoras, advised that all our discourse should begin with a reference to Thales (D.L. II.4).

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Doubts have always existed about whether Thales wrote anything, but a number of ancient reports credit him with writings. Simplicius (Diels, Dox. p. 475) specifically attributed to Thales authorship of the so-called Nautical Star-guide. Diogenes Laertius raised doubts about authenticity, but wrote that 'according to others [Thales] wrote nothing but two treatises, one On the Solstice and one On the Equinox' (D.L. I.23). Lobon of Argus asserted that the writings of Thales amounted to two hundred lines (D.L. I.34), and Plutarch associated Thales with opinions and accounts expressed in verse (Plutarch, De Pyth. or. 18. 402 E). Hesychius, recorded that '[Thales] wrote on celestial matters in epic verse, on the equinox, and much else' (DK, 11A2). Callimachus credited Thales with the sage advice that navigators should navigate by Ursa Minor (D.L. I.23), advice which may have been in writing.

Diogenes mentions a poet, Choerilus, who declared that '[Thales] was the first to maintain the immortality of the soul' (D.L. I.24), and in De Anima, Aristotle's words 'from what is recorded about [Thales]', indicate that Aristotle was working from a written source. Diogenes recorded that '[Thales] seems by some accounts to have been the first to study astronomy, the first to predict eclipses of the sun and to fix the solstices; so Eudemus in his History of Astronomy. It was this which gained for him the admiration of Xenophanes and Herodotus and the notice of Heraclitus and Democritus' (D.L. I.23). Eudemus who wrote a History of Astronomy, and also on geometry and theology, must be considered as a possible source for the hypotheses of Thales. The information provided by Diogenes is the sort of material which he would have included in his History of Astronomy, and it is possible that the titles On the Solstice, and On the Equinox were available to Eudemus. Xenophanes, Herodotus, Heraclitus and Democritus were familiar with the work of Thales, and may have had a work by Thales available to them.

Proclus recorded that Thales was followed by a great wealth of geometers, most of whom remain as honoured names. They commence with Mamercus, who was a pupil of Thales, and include Hippias of Elis, Pythagoras, Anaxagoras, Eudoxus of Cnidus, Philippus of Mende, Euclid, and Eudemus, a friend of Aristotle, who wrote histories of arithmetic, of astronomy, and of geometry, and many lesser known names. It is possible that writings of Thales were available to some of these men.

Any records which Thales may have kept would have been an advantage in his own work. This is especially true of mathematics, of the dates and times determined when fixing the solstices, the positions of stars, and in financial transactions. It is difficult to believe that Thales would not have written down the information he had gathered in his travels, particularly the geometry he investigated in Egypt and his measuring of the height of the pyramid, his hypotheses about nature, and the cause of change.

Proclus acknowledged Thales as the discoverer of a number of specific theorems (A Commentary on the First Book of Euclid's Elements 65. 8-9; 250. 16-17). This suggests that Eudemus, Proclus's source had before him the written records of Thales's discoveries. How did Thales 'prove' his theorems if not in written words and sketches? The works On the Solstice, On the Equinox, which were attributed to Thales (D.L. I.23), and the 'Nautical Star-guide, to which Simplicius referred, may have been sources for the History of Astronomy of Eudemus (D.L. I.23).

There is no direct evidence that any written material of Thales was available to Plato and Aristotle, but there is a surprisingly long list of early writers who could have known Thales, or had access to his works, and these must be considered as possible sources for Plato, Aristotle, and the philosophers and commentators who followed them. Aristotle's wording, 'Thales says', is assertive wording which suggests a reliable source, perhaps writings of Thales himself. Anaximander and Anaximenes were associates of Thales, and would have been familiar with his ideas. Both produced written work. Anaximander wrote in a poetical style (Theophr. ap. Simpl. Phys. fr. 2), and the writing of Anaximenes was simple and unaffected (D.L. II.3). Other philosophers who were credited with written works, who worked on topics similar to those of Thales, and who may have provided material for later writers, are Heraclitus of Ephesus, Anaxagoras of Clazomenae, Alcmaeon, Hippo of Samos, and Hippias of Elis.

Aristotle defined wisdom as knowledge of certain principles and causes (Metaph. 982 a2-3). He commenced his investigation of the wisdom of the philosophers who preceded him, with Thales, the first philosopher, and described Thales as the founder of natural philosophy (Metaph. 983 b21-22). He recorded: 'Thales says that it is water'. 'it' is the nature, the archê, the originating principle. For Thales, this nature was a single material substance, water. Despite the more advanced terminology which Aristotle and Plato had created, Aristotle recorded the doctrines of Thales in terms which were available to Thales in the sixth century BCE Aristotle made a definite statement, and presented it with confidence. It was only when Aristotle attempted to provide the reasons for the opinions that Thales held, and for the theories that he proposed, that he sometimes displayed caution.

Those who believe that Thales inherited his views from Greek or Near-Eastern sources are wrong. Thales was esteemed in his times as an original thinker, and one who broke with tradition and not as one who conveyed existing mythologies. Aristotle unequivocally recorded Thales's hypothesis on the nature of matter, and proffered a number of conjectures based on observation in favour of Thales's declaration (Metaph. 983 b20-28). His report provided the testimony that Thales supplanted myth in his explanations of the behaviour of natural phenomena. Thales did not derive his thesis from either Greek or non-Greek mythological traditions.

Thales would have been familiar with Homer's acknowledgements of divine progenitors but he never attributed organization or control of the cosmos to the gods. Aristotle recognized the similarity between Thales's doctrine about water and the ancient legend which associates water with Oceanus and Tethys, but he reported that Thales declared water to be the nature of all things. Aristotle pointed to a similarity to traditional beliefs, not a dependency upon them. Aristotle did not call Thales a theologian in the sense in which he designated 'the old poets' (Metaph. 1091 b4) and others, such as Pherecydes, as 'mixed theologians' who did not use 'mythical language throughout' (Metaph. 1091 b9). To Aristotle, the theories of Thales were so obviously different from all that had gone before that they stood out from earlier explanations. Thales's views were not ancient and primitive. They were new and exciting, and the genesis of scientific conjecture about natural phenomena. It was the view for which Aristotle acknowledged Thales as the founder of natural philosophy.

The problem of the nature of matter, and its transformation into the myriad things of which the universe is made, engaged the natural philosophers, commencing with Thales. For his hypothesis to be credible, it was essential that he could explain how all things could come into being from water, and return ultimately to the originating material. It is inherent in Thales's hypotheses that water had the potentiality to change to the myriad things of which the universe is made, the botanical, physiological, meteorological and geological states. In Timaeus, 49B-C, Plato had Timaeus relate a cyclic process. The passage commences with 'that which we now call "water" ', and describes a theory which was possibly that of Thales. Thales would have recognized evaporation, and have been familiar with traditional views, such as the nutritive capacity of mist and ancient theories about spontaneous generation, phenomena which he may have 'observed', just as Aristotle believed he, himself had (Hist. An. 569 b1; Gen. An. 762 a9-763 a34), and about which Diodorus Siculus (I.7.3-5; 1.10.6), Epicurus (ap. Censorinus, D.N. IV.9), Lucretius (De Rerum Natura , V.783-808) and Ovid (Met. I.416-437) wrote.

When Aristotle reported Thales's pronouncement that the primary principle is water, he made a precise statement: 'Thales says that it [the nature of things] is water' (Metaph. 983 b20), but he became tentative when he proposed reasons which might have justified Thales's decision: '[Thales's] supposition may have arisen from observation . . . ' (Metaph. 983 b22). It was Aristotle's opinion that Thales may have observed, 'that the nurture of all creatures is moist, and that warmth itself is generated from moisture and lives by it; and that from which all things come to be is their first principle' (Metaph. 983 b23-25). Then, in the lines 983 b26-27, Aristotle's tone changed towards greater confidence. He declared: 'Besides this, another reason for the supposition would be that the semina of all things have a moist nature . . . ' (Metaph. 983 b26-27). In continuing the criticism of Thales, Aristotle wrote: 'That from which all things come to be is their first principle' (Metaph. 983 b25).

Simple metallurgy had been practised long before Thales presented his hypotheses, so Thales knew that heat could return metals to a liquid state. Water exhibits sensible changes more obviously than any of the other so-called elements, and can readily be observed in the three states of liquid, vapour and ice. The understanding that water could generate into earth is basic to Thales's watery thesis. At Miletus it could readily be observed that water had the capacity to thicken into earth. Miletus stood on the Gulf of Lade through which the Maeander river emptied its waters. Within living memory, older Milesians had witnessed the island of Lade increasing in size within the Gulf, and the river banks encroaching into the river to such an extent that at Priene, across the gulf from Miletus the warehouses had to be rebuilt closer to the water's edge. The ruins of the once prosperous city-port of Miletus are now ten kilometres distant from the coast and the Island of Lade now forms part of a rich agricultural plain. There would have been opportunity to observe other areas where earth generated from water, for example, the deltas of the Halys, the Ister, about which Hesiod wrote (Theogony, 341), now called the Danube, the Tigris-Euphrates, and almost certainly the Nile. This coming-into-being of land would have provided substantiation of Thales's doctrine. To Thales water held the potentialities for the nourishment and generation of the entire cosmos. Aëtius attributed to Thales the concept that 'even the very fire of the sun and the stars, and indeed the cosmos itself is nourished by evaporation of the waters' (Aëtius, Placita, I.3).

It is not known how Thales explained his watery thesis, but Aristotle believed that the reasons he proposed were probably the persuasive factors in Thales's considerations. Thales gave no role to the Olympian gods. Belief in generation of earth from water was not proven to be wrong until A.D. 1769 following experiments of Antoine Lavoisier, and spontaneous generation was not disproved until the nineteenth century as a result of the work of Louis Pasteur.

Thales proposed answers to a number of questions about the earth: the question of its support; its shape; its size; and the cause of earthquakes; the dates of the solstices; the size of the sun and moon.

In De Caelo Aristotle wrote: 'This [opinion that the earth rests on water] is the most ancient explanation which has come down to us, and is attributed to Thales of Miletus (Cael. 294 a28-30). He explained his theory by adding the analogy that the earth is at rest because it is of the nature of wood and similar substances which have the capacity to float on water, although not on air (Cael. 294 a30-b1). In Metaphysics (983 b21) Aristotle stated, quite unequivocally: 'Thales . . . declared that the earth rests on water'. This concept does appear to be at odds with natural expectations, and Aristotle expressed his difficulty with Thales's theory (Cael. 294 a33-294 b6).

Perhaps Thales anticipated problems with acceptance because he explained that it floated because of a particular quality, a quality of buoyancy similar to that of wood. At the busy city-port of Miletus, Thales had unlimited opportunities to observe the arrival and departure of ships with their heavier-than-water cargoes, and recognized an analogy to floating logs. Thales may have envisaged some quality, common to ships and earth, a quality of 'floatiness', or buoyancy. It seems that Thales's hypothesis was substantiated by sound observation and reasoned considerations. Indeed, Seneca reported that Thales had land supported by water and carried along like a boat (Sen. QNat. III.14). Aristotle's lines in Metaphysics indicate his understanding that Thales believed that, because water was the permanent entity, the earth floats on water.

Thales may have reasoned that as a modification of water, earth must be the lighter substance, and floating islands do exist. Herodotus (The Histories, II.156) was impressed when he saw Chemmis, a floating island, about thirty-eight kilometres north-east of Naucratis, the Egyptian trading concession which Thales probably visited. Seneca described floating islands in Lydia: 'There are many light, pumice-like stones of which islands are composed, namely those which float in Lydia' (Sen. QNat., III.25. 7-10). Pliny described several floating islands, the most relevant being the Reed Islands, in Lydia (HN, II.XCVII), and Pliny (the Younger) (Ep. VIII.XX) described a circular floating island, its buoyancy, and the way it moved. Thales could have visited the near-by Reed Islands. He might have considered such readily visible examples to be models of his theory, and he could well have claimed that the observation that certain islands had the capacity to float substantiated his hypothesis that water has the capacity to support earth.

Again it is understood that Thales did not mention any of the gods who were traditionally associated with the simple bodies; we do not hear of Oceanus or Gaia: we read of water and earth. The idea that Thales would have resurrected the gods is quite contrary to the bold, new, non-mythical theories which Thales proposed.

Modern commentators assume that Thales regarded the earth as flat, thin, and circular, but there is no ancient testimony to support that opinion. On the contrary, Aristotle may have attributed knowledge of the sphericity of the earth to Thales, an opinion which was later reported by Aëtius (Aët. III. 9-10) and followed by Ps.-Plutarch (Epit. III.10). Aristotle wrote that some think it spherical, others flat and shaped like a drum (Arist. Cael. 293 b33-294 a1), and then attributed belief in a flat earth to Anaximenes, Anaxagoras, and Democritus (Arist. Cael. 294 b14-15). If following chronological order, Aristotle's words, 'some think it spherical', referred to the theory of Thales. Aristotle then followed with the theory of Thales's immediate Milesian successor, Anaximander, and then reported the flat earth view of Anaximenes, the third of the Milesian natural philosophers.

There are several good reasons to accept that Thales envisaged the earth as spherical. Aristotle used these arguments to support his own view (Arist. Cael. 297 b25-298 a8). First is the fact that during a solar eclipse, the shadow caused by the interposition of the earth between the sun and the moon is always convex; therefore the earth must be spherical. In other words, if the earth were a flat disk, the shadow cast during an eclipse would be elliptical. Second, Thales, who is acknowledged as an observer of the heavens, would have observed that stars which are visible in a certain locality may not be visible further to the north or south, a phenomena which could be explained within the understanding of a spherical earth. Third, from mere observation the earth has the appearance of being curved. From observation, it appears that the earth is covered by a dome. When observed from an elevated site, the sky seems to surround the earth, like a dome, to meet the apparently curved horizon. If observed over the seasons, the dome would appear to revolve, with many of the heavenly bodies changing their position in varying degrees, but returning annually to a similar place in the heavens. Through his work in astronomy Thales would almost certainly have become familiar with the night sky and the motion of the heavenly bodies. There is evidence that he gave advice to navigate by Ursa Minor, and was so involved in observation of the stars that he fell into a well. As a result of observations made over a long period of time, Thales could have realized that the motions of the fixed stars could not be explained within the idea of the observable hemispherical dome. During the determination of the size of the rising sun, and again while watching its risings and settings during his work on fixing the solstices, Thales may have realized that much natural phenomena could be explained only within the understanding of the earth as a sphere.

From the shore, a ship can be seen to be descending, gradually, below the horizon, with the hull disappearing from view first, to be followed by masts and sails. If one had a companion observing from a higher point, the companion would see the ship for a long period before it disappeared from view.

Aëtius recorded the different opinions of the shape of the earth that were held by Thales, Anaximander and Anaximenes (III.9-10; III.10; and III.10). Cicero attributed to Thales the earliest construction of a solid celestial globe (Rep. I.XIII.22). Thales's immediate successors proposed theories about the shape of the earth which were quite different from each other, but that is no reason to reject the view that Thales hypothesized a spherical earth. It is not the only occasion on which Anaximander and Anaximenes failed to follow the theories of Thales. That they did not do so is the main argument in favour of accepting that the scientific method commenced in the Milesian School. There is testimony that Thales knew the earth to be spherical, but no evidence to suggest that he proposed any other shape.

Thales's theory about the cause of earthquakes is consistent with his hypothesis that earth floats upon water. It seems that he applied his floating on water simile to the natural phenomena of earthquakes. Aëtius recorded that Thales and Democritus found in water the cause of earthquakes (Aët. III.15), and Seneca attributed to Thales a theory that on the occasions when the earth is said to quake it is fluctuating because of the roughness of oceans (QNat. III.14; 6.6). Although the theory is wrong, Thales's hypothesis is rational because it provides an explanation which does not invoke hidden entities. It is an advance upon the traditional Homeric view that they resulted from an angry supernatural god, Poseidon, shaking the earth through his rapid striding.

The question of whether Thales endowed the gods with a role in his theories is fundamental to his hypotheses. The relevant text from Aristotle reads: 'Thales, too, to judge from what is recorded of his views, seems to suppose that the soul is in a sense the cause of movement, since he says that a stone [magnet, or lodestone] has a soul because it causes movement to iron' (De An. 405 a20-22); 'Some think that the soul pervades the whole universe, whence perhaps came Thales's view that everything is full of gods' (De An. 411 a7-8). In reference to the clause in the first passage 'to judge from what is recorded of his views', Snell convincingly argued that Aristotle had before him the actual sentence recording Thales's views about the lodestone (Snell, 1944, 170). In the second passage the 'some' to whom Aristotle refers are Leucippus, Democritus, Diogenes of Apollonia, Heraclitus, and Alcmaeon, philosophers who were later than Thales. They adopted and adapted the earlier view of Thales that soul was the cause of motion, permeating and enlivening the entire cosmos. The order in which Aristotle discussed Thales's hypothesis obscures the issue.

The source for Aristotle's report that Thales held all things to be full of gods is unknown, but some presume that it was Plato. Thales is not mentioned in the relevant lines in Plato, but there is a popular misconception that they refer to the belief of Thales. This is wrong. Thales had rejected the old gods. In a passage in Apology(26 C) Socrates identified the heavenly bodies as gods, and pointed out that that was the general understanding. In Cratylus(399 D-E) Plato had Socrates explain a relationship between soul as a life-giving force, the capacity to breathe, and the reviving force. In Timaeus 34B) Plato had Timaeus relate a theory which described soul as pervading the whole universe. Then, in Laws Plato has the Athenian Stranger say: 'Everyone . . . who has not reached the utmost verge of folly is bound to regard the soul as a god. Concerning all the stars and the moon, and concerning the years and months and all seasons, what other account shall we give than this very same, - namely, that, inasmuch as it has been shown that they are all caused by one or more souls . . . we shall declare these souls to be gods . . .? Is there any man that agrees with this view who will stand hearing it denied that 'all things are full of gods'? The response is: 'No man is so wrong-headed as that' (Laws, 899 A-B). Plato had the Athenian Stranger extend his ideas into a theological theory. He used a sleight of hand method to express his own ideas about divine spiritual beings. With the exception of gods in the scheme of things, these passages reflect the beliefs which formed the Thalean hypothesis, but Plato did not have the Athenian Stranger attribute the crucial clause 'all things are full of gods' to Thales. Thales is not mentioned.

Aristotle's text not the earliest extant testimony. Diogenes preserved a report from Hippias: 'Aristotle and Hippias affirm that, arguing from the magnet and from amber, [Thales] attributed a soul or life even to inanimate objects' (D.L. I.24). This early report does not mention godly entities. The later commentators, Cicero (Nat. D. I.X.25), and Stobaeus (Ecl. I.1.11) included gods in Thales's theory. However, their views post-date Stoicism and are distorted by theistic doctrines.

Plato converted the idea of soul into a theory that 'all things are full of gods', and this may have been Aristotle's source, but the idea of gods is contrary to Thales's materialism. When Thales defined reality, he chose an element, not a god. The motive force was not a supernatural being. It was a force within the universe itself. Thales never invoked a power that was not present in nature itself, because he believed that he had recognized a force which underpinned the events of nature.

Thales is acclaimed for having predicted an eclipse of the sun which occurred on 28 May 585 BCE The earliest extant account of the eclipse is from Herodotus: 'On one occasion [the Medes and the Lydians] had an unexpected battle in the dark, an event which occurred after five years of indecisive warfare: the two armies had already engaged and the fight was in progress, when day was suddenly turned into night. This change from daylight to darkness had been foretold to the Ionians by Thales of Miletus, who fixed the date for it within the limits of the year in which it did, in fact, take place' (Hdt. I.74). The vital points are: Thales foretold a solar eclipse; it did occur within the period he specified. How Thales foretold the eclipse is not known but there is strong opinion that he was able to perform this remarkable feat through knowledge of a cycle known as the Saros, with some attributing his success to use of the Exeligmos cycle. It is not known how Thales was able to predict the Eclipse, if indeed he did, but he could not have predicted the Eclipse by using the Saros or the Exeligmos cycles.

In addition to Herodotus, the successful prediction of the eclipse was accepted by Eudemus in his History of Astronomy and acknowledged by a number of other writers of ancient times (Cicero, Pliny, Dercyllides, Clement, Eusebius). This is how Diogenes Laertius recorded the event: '[Thales] seems by some accounts to have been the first to study astronomy, the first to predict eclipses of the sun, and to fix the solstices; so Eudemus in his History of Astronomy. It was this which gained for him the admiration of Xenophanes and Herodotus and the notice of Heraclitus and Democritus' (D.L. I.23). Diogenes asserted that Herodotus knew of Thales's work, and in naming Xenophanes, Heraclitus, and Democritus, he nominated three of the great pre-Socratics, eminent philosophers who were familiar with the work of Thales.

Modern astronomy confirms that the eclipse did occur, and was total. According to Herodotus's report, the umbra of the eclipse of Thales must have passed over the battle field. The "un-naturalness" of a solar eclipse is eerie and chilling. All becomes hushed and there is a strong uncanny sensation of impending disaster, of being within the control of some awful power. In ancient times, the awesome phenomenon must have aroused great fear, anxiety and wonder. The combatants saw the eclipse as disapproval of their warfare, and as a warning. They ceased fighting and a peace agreement was reached between the two kings.

It is not known why Thales turned away from the traditional beliefs which attributed all natural events and man's fortunes and misfortunes to the great family of Olympian gods, but Miletus was the most prosperous of the Ionian cities, and it cannot be doubted that the flourishing merchants believed that their prosperity resulted from their own initiative and endeavours. Thales's great philosophical pronouncement that water is the basic principle shows that Thales gave no acknowledgement to the gods as instigators and controllers of phenomena. Thales's hypotheses indicate that he envisaged phenomena as natural events with natural causes and possible of explanation. From his new perspective of observation and reasoning, Thales studied the heavens and sought explanations of heavenly phenomena.

It is widely accepted that Thales acquired information from Near-Eastern sources and gained access to the extensive records which dated from the time of Nabonassar (747 BCE) and which were later used by Ptolemy (Alm. III.7. H 254). Some commentators have suggested that Thales predicted the solar eclipse of 585 BCE through knowledge of the Saros period, a cycle of 223 lunar months (18 years, 10-11 days plus 0.321124 of a day) after which eclipses both of the sun and moon repeat themselves with very little change, or through knowledge of the Exeligmos cycle which is exactly three times the length of the Saros (Ptolemy, Alm. IV.2. H270). The ancients could not have predicted solar eclipses on the basis of those periodic cycles because eclipses of the sun do not repeat themselves with very little change. The extra 0.321124 of a day means that each recurring solar eclipse will be visible to the west, just under one-third of the circumference of the earth, being a period of time of almost 7.7 hours. This regression to the west could not have been known to the ancient astrologers, a fact which seems not to have been taken into account by the philosophers who attribute Thales's success to application of one of those two cycles.

The following important fact should be noted. Some commentators and philosophers believe that Thales may have witnessed the solar eclipse of 18th May 603 BCE or have had heard of it. They accepted that he had predicted the solar eclipse of 28 May 585 BCE and reasoned from the astronomical fact of the Saros cycles and the fact that the two solar eclipses had been separated by the period of 18 years, 10 days, and 7.7 hours, and concluded that Thales had been able to predict a solar eclipse based upon the knowledge of that cycle. Two facts discount rebut those claims. First, recent research shows that the solar eclipse of 18th May 603 BCE would not have been visible in Egypt, nor in the Babylonian observation cities where the astronomers watched the heavens for expected and unusual heavenly events. The eclipse of 603 passed over the Persian Gulf, too far to the south for observation (Stephenson, personal communication, March 1999; and Stephenson, "Long-term Fluctuations", 165-202). Even if the eclipse of 603 had been visible to the Near-Eastern astronomers, it is not possible to recognize a pattern from witnessing one event, or indeed, from witnessing two events. One may suggest a pattern after witnessing three events that are separated by equal periods of time, but the eclipse which preceded that of 603, and which occurred on 6th May 621, was not visible in Near-Eastern regions. Consequently, it could not have been recorded by the astrologer/priests who watched for unusual heavenly phenomena, and could not have been seen as forming a pattern.

It is quite wrong to say that eclipses repeat themselves with very little change, because each solar eclipse in a particular Saros occurs about 7.7 hours later than in the previous eclipse in the same Saros, and that is about ¹/₃ of the circumference of the earth's circumference. Adding to the difficulty of recognizing a particular cycle is the fact that about forty-two periodic cycles are in progress continuously, and overlapping at any time. Every series in a periodic cycle lasts about 1,300 years and comprises 73 eclipses. Eclipses which occur in one periodic cycle are unrelated to eclipses in other periodic cycles.

The ancient letters prove that the Babylonians and Assyrians knew that lunar eclipses can occur only at full moon, and solar eclipses only at new moon, and also that eclipses occur at intervals of five or six months. However, while lunar eclipses are visible over about half the globe, solar eclipses are visible from only small areas of the earth's surface. Recent opinion is that, as early as 650 BCE the Assyrian astronomers seem to have recognized the six months-five months period by which they could isolate eclipse possibilities (Steele, "Eclipse Prediction", 429).

In other recent research Britton has analysed a text known as Text S, which provides considerable detail and fine analysis of lunar phenomena dating from Nabonassar in 747 BCE The text points to knowledge of the six-month five month periods. Britton believes that the Saros cycle was known before 525 BCE (Britton, "Scientific Astronomy", 62) but, although the text identifies a particular Saros cycle, and graphically depicts the number of eclipse possibilities, the ancient commentary of Text S does not attest to an actual observation (Britton, "An Early Function", 32).

There is no evidence that the Saros could have been used for the prediction of solar eclipses in the sixth century BCE, but it remains possible that forthcoming research, and the transliteration of more of the vast stock of ancient tablets will prove that the Babylonians and Assyrians had a greater knowledge of eclipse phenomena than is now known.

The Babylonian and Assyrian astronomers knew of the Saros period in relation to lunar eclipses, and had some success in predicting lunar eclipses but, in the sixth century BCE when Thales lived and worked, neither the Saros nor the Exeligmos cycles could be used to predict solar eclipses.

It is testified that Thales knew that the sun is eclipsed when the moon passes in front of it, the day of eclipse - called the thirtieth by some, new moon by others (The Oxyrhynchus Papyri, 3710). Aëtius (II.28) recorded: [Thales] says that eclipses of the sun take place when the moon passes across it in a direct line, since the moon is earthy in character; and it seems to the eye to be laid on the disc of the sun'.

There is a possibility that, through analysis of ancient eclipse records, Thales identified another cycle, the lunar eclipse-solar eclipse cycle of 23 ¹/₂ months, the fact that a solar eclipse is a possibility 23 ¹/₂ months after a lunar eclipse. However, lunar eclipses are not always followed by solar eclipses. Although the possibility is about 57% it is important to note that the total solar eclipse of 28th May, 585, occurred 23 ¹/₂months after the total lunar eclipse of 4th July, 587. The wording of the report of the eclipse by Herodotus: 'Thales . . . fixed the date for the eclipse within the limits of the year' is precise, and suggests that Thales's prediction was based upon a definite eclipse theory.

A report from Theon of Smyrna ap. Dercyllides states that: 'Eudemus relates in the Astronomy that Thales was the first to discover the eclipse of the sun and that its period with respect to the solstices is not always constant' (DK, 11 A 17). Diogenes Laertius (I.24) recorded that [Thales] was the first to determine the sun's course from solstice to solstice, and also acknowledged the Astronomy of Eudemus as his source.

Solstices are natural phenomena which occur on June 21 or 22, and December 21 or 22, but the determination of the precise date on which they occur is difficult. This is because the sun seems to 'stand still' for several days because there is no discernible difference in its position in the sky. It is the reason why the precise determination of the solstices was so difficult. It was a problem which engaged the early astronomers, and more than seven centuries later, Ptolemy acknowledged the difficulty (Alm. III.1. H203).

It is not known how Thales proceeded with his determination, but the testimony of Flavius Philostratus is that: '[Thales] observed the heavenly bodies . . . from [Mount] Mycale which was close by his home' (Philostratus, Life of Apollonius , II.V). This suggests that Thales observed the rising and setting of the sun for many days at mid-summer and mid-winter (and, necessarily, over many years). Mount Mycale, being the highest point in the locality of Miletus, would provide the perfect vantage point from which to make observations. Another method which Thales could have employed was to measure the length of the noon-day sun around mid-summer and mid-winter. Again this would require observations to be made, and records kept over many days near the solstice period, and over many years.

From Diogenes Laertius we have the report: '[Thales] is said to have discovered the seasons of the year and divided it into 365 days' (D.L. I.27). Because Thales had determined the solstices, he would have known of the number of days between say, summer solstices, and therefore have known the length of a solar year. It is consistent with his determination of the solstices that he should be credited with discovering that 365 days comprise a year. It is also a fact that had long been known to the Egyptians who set their year by the more reliable indicator of the annual rising of the star Sirius in July. Thales may have first gained the knowledge of the length of the year from the Egyptians, and perhaps have attempted to clarify the matter by using a different procedure. Thales certainly did not 'discover' the seasons, but he may have identified the relationship between the solstices, the changing position during the year of the sun in the sky, and associated this with seasonal climatic changes.

Apuleius wrote that 'Thales in his declining years devised a marvellous calculation about the sun, showing how often the sun measures by its own size the circle which it describes'. (Apul. Florida, 18). Following soon after Apuleius, Cleomedes explained that the calculation could be made by running a water-clock, from which the result was obtained: the diameter of the sun is found to be one seven-hundred-and-fiftieth of its own orbit (Cleomedes, De Motu circulari corporum caelestium, II.75). The third report is from Diogenes: 'According to some [Thales was] the first to declare the size of the sun to be one seven hundred and twentieth part of the solar circle, and the size of the moon to be the same fraction of the lunar circle' (D.L. I.24). Little credence can be given to the water-clock method for reaching this determination, because there is an inbuilt likelihood of repeated errors over the 24 hour period. Even Ptolemy, who flourished in the second century A.D., rejected all measurements which were made by means of water-clocks, because of the impossibility of attaining accuracy by such means (Alm. V.14. H416).

In his work in geometry, Thales was engaged in circles and angles, and their characteristics, and he could have arrived at his solution to the problem by applying the geometrical knowledge he had acquired. There is no evidence to support a suggestion that Thales was familiar with measurements by degrees but he could have learnt, from the Babylonians, that a circle is divided into 3600. The figure of 720, which was given by Diogenes for Thales, is double 360, and this is related to the Babylonian sexagesimal system. To establish the dates of the solstices, Thales probably made repeated observations of the risings and settings of the sun. From such experiments he could have observed that the angle which was subtended by the elevation of the rising sun is 1/20 and with 3600 in a circle, the ratio of 1:720 is determined.

Of the report from Diogenes Laertius (D.L. I.24) that Thales also determined the orbit of the moon in relation to the size of its diameter, Thales would repeat the method to calculate the orbit of the moon.

Callimachus (D.L. I.22) reported that Thales 'discovered' Ursa Minor. This means only that he recognized the advantages of navigating by Ursa Minor, rather than by Ursa Major, as was the preferred method of the Greeks. Ursa Minor, a constellation of six stars, has a smaller orbit than does the Great Bear, which means that, as it circles the North Pole, Ursa Minor changes its position in the sky to a lesser degree than does the Great Bear. Thales offered this sage advice to the mariners of Miletus, to whom it should have been of special value because Miletus had developed a maritime trade of economic importance.

In Theaetetus (174 A) Plato had Socrates relate a story that Thales was so intent upon watching the stars that he failed to watch where he was walking, and fell into a well. The story is also related by Hippolytus (Diels, Dox. 555), and by Diogenes Laertius (D.L. II.4-5). Irony and jest abound in Plato's writing and he loved to make fun of the pre-Socratics, but he is not likely to have invented the episode, especially as he had Socrates relate the event. Aristotle wrote that viewing the heavens through a tube 'enables one to see further' (Gen. An. 780 b19-21), and Pliny (HN, II.XI) wrote that: 'The sun's radiance makes the fixed stars invisible in daytime, although they are shining as much as in the night, which becomes manifest at a solar eclipse and also when the star is reflected in a very deep well'. Thales was renowned and admired for his astronomical studies, and he was credited with the 'discovery' of Ursa Minor (D.L. I.23). If Thales had heard that stars could be viewed to greater advantage from wells, either during day or night, he would surely have made an opportunity to test the theory, and to take advantage of a method that could assist him in his observations. The possibility that the story was based on fact should not be overlooked. Plato had information which associated Thales with stars, a well, and an accident. Whether Thales fell into a well, or tripped when he was getting in or out of a well, the story grew up around a mishap.

The practical skill of land measurement was invented in Egypt because of the necessity frequently to remeasure plots of land after destructive inundations. The phenomena is well described by Herodotus (II.93-109). Egypt was believed to be the source of much wisdom and reports tell us that many Greeks, including Thales, Pythagoras, Solon, Herodotus, Plato, Democritus, and Euclid, visited that ancient land to see the wonders for themselves.

>The Egyptians had little to offer in the way of abstract thought. The surveyors were able to measure and to calculate and they had outstanding practical skills. In Egypt Thales would have observed the land surveyors, those who used a knotted cord to make their measurements, and were known as rope-stretchers. Egyptian mathematics had already reached its heights when The Rhind Mathematical Papyrus was written in about 1800 BCE More than a thousand years later, Thales would have watched the surveyors as they went about their work in the same manner, measuring the land with the aid of a knotted rope which they stretched to measure lengths and to form angles.

The development of geometry is preserved in a work of Proclus, A Commentary on the First Book of Euclid's Elements (64.12-65.13). Proclus provided a remarkable amount of intriguing information, the vital points of which are the following: Geometry originated in Egypt where it developed out of necessity; it was adopted by Thales who had visited Egypt, and was introduced into Greece by him

The Commentary of Proclus indicates that he had access to the work of Euclid and also to The History of Geometry which was written by Eudemus of Rhodes, a pupil of Aristotle, but which is no longer extant. His wording makes it clear that he was familiar with the views of those writers who had earlier written about the origin of geometry. He affirmed the earlier views that the rudiments of geometry developed in Egypt because of the need to re-define the boundaries, just as Herodotus stated.

Five Euclidean theorems have been explicitly attributed to Thales, and the testimony is that Thales successfully applied two theorems to the solution of practical problems.

Thales did not formulate proofs in the formal sense. What Thales did was to put forward certain propositions which, it seems, he could have 'proven' by induction: he observed the similar results of his calculations: he showed by repeated experiment that his propositions and theorems were correct, and if none of his calculations resulted in contrary outcomes, he probably felt justified in accepting his results as proof. Thalean 'proof' was often really inductive demonstration. The process Thales used was the method of exhaustion. This seems to be the evidence from Proclus who declared that Thales 'attacked some problems in a general way and others more empirically'.

DEFINITION I.17: A diameter of the circle is a straight line drawn through the centre and terminated in both directions by the circumference of the circle; and such a straight line also bisects the circle (Proclus, 124). >

PROPOSITION I.5: In isosceles triangles the angles at the base are equal; and if the equal straight lines are produced further, the angles under the base will be equal (Proclus, 244). It seems that Thales discovered only the first part of this theorem for Proclus reported: We are indebted to old Thales for the discovery of this and many other theorems. For he, it is said, was the first to notice and assert that in every isosceles the angles at the base are equal, though in somewhat archaic fashion he called the equal angles similar (Proclus, 250.18-251.2).

PROPOSITION I.15: 'If two straight lines cut one another, they make the vertical angles equal to one another' (Proclus, 298.12-13). This theorem is positively attributed to Thales. Proof of the theorem dates from the Elements of Euclid (Proclus, 299.2-5).

PROPOSITION I.26: 'If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely, either the side adjoining the equal angles, or that subtending one of the equal angles, they will also have the remaining sides equal to the remaining sides and the remaining angle equal to the remaining angle' (Proclus, 347.13-16). 'Eudemus in his history of geometry attributes the theorem itself to Thales, saying that the method by which he is reported to have determined the distance of ships at sea shows that he must have used it' (Proclus, 352.12-15). Thales applied this theorem to determine the height of a pyramid. The great pyramid was already over two thousand years old when Thales visited Gizeh, but its height was not known. Diogenes recorded that 'Hieronymus informs us that [Thales] measured the height of the pyramids by the shadow they cast, taking the observation at the hour when our shadow is of the same length as ourselves' (D.L. I.27). Pliny (HN, XXXVI.XVII.82) and Plutarch (Conv. sept. sap. 147) also recorded versions of the event. Thales was alerted by the similarity of the two triangles, the 'quality of proportionality'. He introduced the concept of ratio, and recognized its application as a general principle. Thales's accomplishment of measuring the height of the pyramid is a beautiful piece of mathematics. It is considered that the general principle in Euclid I.26 was applied to the ship at sea problem, would have general application to other distant objects or land features which posed difficulties in the calculation of their distances.

PROPOSITION III.31: 'The angle in a semicircle is a right angle'. Diogenes Laertius (I.27) recorded: 'Pamphila states that, having learnt geometry from the Egyptians, [Thales] was the first to inscribe a right-angled triangle in a circle, whereupon he sacrificed an ox'. Aristotle was intrigued by the fact that the angle in a semi-circle is always right. In two works, he asked the question: 'Why is the angle in a semicircle always a right angle?' (An. Post. 94 a27-33; Metaph. 1051 a28). Aristotle described the conditions which are necessary if the conclusion is to hold, but did not add anything that assists with this problem.

It is testified that it was from Egypt that Thales acquired the rudiments of geometry. However, the evidence is that the Egyptian skills were in orientation, measurement, and calculation. Thales's unique ability was with the characteristics of lines, angles and circles. He recognized, noticed and apprehended certain principles which he probably 'proved' through repeated demonstration.

Herodotus recorded 'the general belief of the Greeks' that Thales assisted Croesus in transporting his troops across the Halys river (Hdt. I.75) on his advance into Capadoccia to engage the great Persian conqueror, Cyrus who threatened from the east. Herodotus provided a detailed description of the reported crossing which many of the Greeks supposed had been accomplished through Thales's engineering skills and ingenuity (Hdt. I.75). Herodotus had been told that Thales advised Croesus to divide the river into two parts. The story is that Thales directed the digging so that the river was diverted into two smaller streams, each of which could then be forded. The story from Herodotus describes a formation similar to an oxbow lake. The work could have been undertaken by the men of Croesus's army, and directed by Thales. With both channels then being fordable, Croesus could lead his army across the Halys. This description complies with 'the general belief of the Greeks' which Herodotus related.

However, Herodotus did not accept that story, because he believed that bridges crossed the river at that time (I.74). Herodotus's misgivings were well founded. There is considerable support for the argument that Croesus and his army crossed the Halys by the bridge which already existed and travelled by the Royal Road which provided the main access to the East. Herodotus explained that at the Halys there were gates which had to be passed before one crossed the river, which formed the border, with the post being strongly guarded (Hdt. V.52).

The town of Cesnir Kopru, or Tcheshnir Keupreu, is a feasible site for a crossing. Before the industrialization of the area, a mediaeval bridge was observed, underneath which, when the river was low, could be seen not only the remains of its Roman predecessor but the roughly hewn blocks of a much earlier bridge (Garstang, 1959, 2). Any clues that may have helped to provide an answer to the question of whether there were bridges in the time of Croesus are now submerged by the hydroelectric plants which have been built in the area. Herodotus recorded the details that he had obtained, but used his own different understanding of the situation to discount the report.

Establishing whether or not Thales travelled and what countries he visited is important because we may be able to establish what information he could have acquired from other sources. In Epinomis 987 E) Plato made the point that the Greeks took from foreigners what was of value and developed their notions into better ideas.

Eudemus, who was one of Aristotle's students, believed that Thales had travelled to Egypt (Eudemus ap. Proclus, 65.7). A number of ancient sources support that opinion, including Pamphila who held that he spent time with the Egyptian priests (D.L. I.24), Hieronymus from whose report we learn that Thales measured the height of the pyramids by the shadow they cast (D.L. I.27), and Plutarch (De Is. et Os. 131). Thales gave an explanation for the inundation (D.L. I.37). He may have devised this explanation after witnessing the phenomena, which Herodotus later described (Hdt. II.97).

By 620 BCE, and perhaps earlier, Miletus held a trading concession at Naucratis (Hdt. II.178, Strab. 17.1.18) on the Canopic mouth of the Nile, and it is possible that Thales visited Egypt on a trading mission. Travel to Egypt would not have been difficult. Homer had Ulysses sailing from Crete to the Nile in five days, and Ernle Bradford recently made a similar journey, proving the trip to be feasible (Bradford, Ulysses Found, 26, and passim). The wealth of Miletus was the result of its success as a trading centre, and there would have been no difficulty in arranging passage on one of the many vessels which traded through of Miletus.

Josephus (Contra Apionem I.2) wrote that Thales was a disciple of the Egyptians and the Chaldeans which suggests that he visited the Near-East. It is thought that Thales visited the Babylonians and Chaldeans and had access to the astrological records which enabled him to predict the solar eclipse of 585 BCE

Miletus had founded many colonies around the Mediterranean and especially along the coasts of the Black Sea. Pliny (HN, V.31.112) gives the number as ninety. The Milesians traded their goods for raw materials, especially iron and timber, and tunny fish. Strabo made mention of 'a sheep-industry', and the yield of 'soft wool' (Strabo, 12.3.13), and Aristophanes mentioned the fine and luxurious Milesian wool (Lysistrata, 729; Frogs, 543). The Milesian traders had access to the hinterland. The land around the mouth of the Halys was fertile, 'productive of everything . . . and planted with olive trees' (Strabo, 12.3.12-13). Thales was associated with a commercial venture in the production of olive oil in Miletus and Chios, but his interests may have extended beyond those two places. Olive oil was a basic item in the Mediterranean diet, and was probably a trading commodity of some importance to Milesian commerce.

It is likely that Thales was one of the 'great teachers' who, according to Herodotus, visited Croesus in the Lydian capital, Sardis (Hdt. I.30). From Sardis, he could have joined a caravan to make the three-month journey along the well used Royal Road (Hdt. V.53), to visit the observatories in Babylonia, and seek the astronomical knowledge which they had accumulated over centuries of observation of heavenly phenomena. In about 547 BCE late in his life, Thales travelled into Cappadocia with Croesus, and, according to some belief, devised a scheme by which the army of Croesus was able to cross the River Halys. Milesian merchantmen continually plied the Black Sea, and gaining a passage could have been easily arranged. From any number of ports Thales could have sought information, and from Sinope he may have ventured on the long journey to Babylonia, perhaps travelling along the valley of the Tigris, as Xenophon did in 401-399 BCE

In a letter purported to be from Thales to Pherecydes, Thales stated that he and Solon had both visited Crete, and Egypt to confer with the priests and astronomers, and all over Hellas and Asia (D.L. I.43-44). All that should be gleaned from such reports, is that travel was not exceptional, with many reports affirming the visits of mainly notable people to foreign lands. Alcaeus visited Egypt' (Strabo, 1.2.30), and his brother, Antimenidas, served in Judaea in the army of the Babylonian monarch, King Nebuchadrezzar. Sappho went into exile in Sicily, her brother,Charaxus, spent some time in Egypt, and a number of friends of Sappho visited Sardis where they lived in Lydian society. There must have been any number of people who visited foreign lands, about whom we know nothing.

Very little about the travels of Thales may be stated with certainty, but it seems probable that he would have sought information from any sources of knowledge and wisdom, particularly the centres of learning in the Near-East. It is accepted that there was ample opportunity for travel.

Thales was the founder of a new school of philosophy (Arist. Metaph. 983 b20). His two fellow Milesians who also engaged in the new questioning approach to the understanding of the universe, were Anaximander, his disciple (D.L. I.13), and Anaximenes, who was the disciple of Anaximenes (D.L. II.2). Anaximander was about ten years younger than Thales, but survived him by only a year, dying in about 545. Anaximenes was born in 585 and died in about 528. Their lives all overlapped. Through their association they comprised the Milesian School: They all worked on similar problems, the nature of matter and the nature of change, but they each proposed a different material as the primary principle, which indicates that there was no necessity to follow the master's teachings or attribute their discoveries to him. Each proposed a different support for the earth. Thales was held in high regard for his wisdom, being acclaimed as the most eminent of the Wise Men of Ancient Greece, but he was not regarded as a god, as Pythagoras was. Anaximander and Anaximenes were free to pursue their own ideas and to express them in writing. This surely suggests that they engaged in critical discussion of the theories of each other. The Greeks are a sociable people, and their willingness to converse brought rewards in knowledge gained, as Plato remarked (Epinomis, 987E). Critical discussion implies more than familiarity with other views, and more than mere disagreement with other theories. It is the adoption, or in this case, the development, of a new style of discussion. It is a procedure which encourages questioning, debate, explanation, justification and criticism. There was a unique relationship between the three Milesians and it is highly probable that the critical method developed in the Milesian School under the leadership of Thales.

The earliest reference to the Seven Sages of Ancient Greece is in Plato's Protagoras in which he listed seven names: 'A man's ability to utter such remarks [notable, short and compressed] is to be ascribed to his perfect education. Such men were Thales of Miletus, Pittacus of Mitylene, Bias of Priene, Solon of our city [Athens], Cleobulus of Lindus, Myson of Chen, and, last of the traditional seven, Chilon of Sparta. . . . and you can recognize that character in their wisdom by the short memorable sayings that fell from each of them' (Protagoras, 342 E-343 A).

Diogenes recorded that 'Thales was the first to receive the name of Sage in the archonship of Damasias at Athens, when the term was applied to all the Seven Sages, as Demetrius of Phalerum [born. ca. 350 B.C] mentions in his List of Archons (D.L. I.22). Demetrius cannot have been the source for Plato, who died when Demetrius was only three years old. Perhaps there was a source common to both Plato and Demetrius, but it is unknown.

Damasias was archon in 582/1. It may be significant that at this time the Pythian Games were re-organized. More events were added and, for the first time, they were to be held at intervals of four years, in the third year of the Olympiad, instead of the previous eight-yearly intervals. Whether there is an association between the re-organization of the Pythian Games and the inauguration of the Seven Sages in not known but, as Pausanias indicates, the Seven were selected from all around Greece: 'These [the sages] were: from Ionia, Thales of Miletus and Bias of Priene; of the Aeolians in Lesbos, Pittacus of Mitylene; of the Dorians in Asia, Cleobulus of Lindus; Solon of Athens and Chilon of Sparta; the seventh sage, according to the list of Plato, the son of Ariston is not Periander, the son of Cypselus, but Myson of Chenae, a village on Mount Oeta' (Paus. 14.1). The purpose of Damasias may have been aimed at establishing unity between the city-states.

It is difficult to believe that the Seven all assembled at Delphi, although the dates just allow it. Plato wrote that their notable maxims were featured at Delphi: 'They [the Sages], assembled together and dedicated these [short memorable sayings] as the first-fruits of their lore to Apollo in his Delphic temple, inscribing there those maxims which are on every tongue - "Know thyself' and "Nothing overmuch" ' (Pl. Prt. 343 A-B).

Plato regarded wise maxims as the most essential of the criteria for a sage, and associated them with wisdom and with good education, but he has Socrates say: 'Think again of all the ingenious devices in arts or other achievements, such as you might expect in one of practical ability; you might remember Thales of Miletus and Anacharsis the Scythian' (Respublica , 600 A). Practical ability was clearly important.

Several other lists were compiled: Hippobotus (D.L. I.42); Pittacus (D.L. I.42); and Diogenes (D.L. I.13. They omitted some names and adding others. In his work On the Sages, Hermippus reckons seventeen, which included most of the names listed by other compilers.

Many commentators state that Thales was named as Sage because of the practical advice he gave to Miletus in particular, and to Ionia in general. The earlier advice was to his fellow Milesians. In 560, the thirty-five year old Croesus (Hdt. I.25) succeeded his father Alyattes and continued the efforts begun by his father to subdue the Milesians, but without success. Diogenes tells us that 'when Croesus sent to Miletus offering terms of alliance, [Thales] frustrated the plan' (D.L. I.25). The second occasion was at an even later date, when the power of Cyrus loomed as a threat from the east. Thales's advice to the Ionian states was to unite in a political alliance, so that their unified strength could be a defence against the might of Cyrus. This can hardly have been prior to 550 BCE which is thirty years later than the promulgation of the Seven Sages. Thales was not named as a Sage because of any political advice which is extant.

One of the few dates in Thales's life which can be known with certainty is the date of the Eclipse of 585 BCE It brought to a halt the battle being fought between Alyattes and the Mede, Cyaxares and, in addition, brought peace to the region after 'five years of indecisive warfare' (Hdt. I.74). The Greeks believed that Thales had predicted the Eclipse, and perhaps even regarded him as being influential in causing the phenomenon to occur. This was reason enough to declare Thales to be a man of great wisdom and to designate him as the first of the Seven Sages of Ancient Greece.

Thales's reputation for wisdom is further enhanced in a story which was related by Aristotle. (Politics, 1259 a 6-23). Somehow, through observation of the heavenly bodies, Thales concluded that there would be a bumper crop of olives. He raised the money to put a deposit on the olive presses of Miletus and Chios, so that when the harvest was ready, he was able to let them out at a rate which brought him considerable profit. In this way, Thales answered those who reproached him for his poverty. As Aristotle points out, the scheme has universal application, being nothing more than a monopoly. There need not have been a bumper harvest for the scheme to have been successful. It is quite likely that Thales was involved in commercial ventures, possibly the export of olive oil, and Plutarch reported that Thales was said to have engaged in trade (Plut. Vit. Sol. II.4).

Thales is the first person about whom we know to propose explanations of natural phenomena which were materialistic rather than mythological or theological. His theories were new, bold, exciting, comprehensible, and possible of explanation. He did not speak in riddles as did Heraclitus, and had no need to invent an undefined non-substance, as Anaximander did. Because he gave no role to mythical beings, Thales's theories could be refuted. Arguments could be put forward in attempts to discredit them. Thales's hypotheses were rational and scientific. Aristotle acknowledged Thales as the first philosopher, and criticized his hypotheses in a scientific manner.

The most outstanding aspects of Thales's heritage are: The search for knowledge for its own sake; the development of the scientific method; the adoption of practical methods and their development into general principles; his curiosity and conjectural approach to the questions of natural phenomena - In the sixth century BCE Thales asked the question, 'What is the basic material of the cosmos?' The answer is yet to be discovered.

Britton, John P. "An Early Function for Eclipse Magnitudes in Babylonian Astronomy." Centaurus, 32 (1989): 32.

Britton, John P. "Scientific Astronomy in Pre-Seleucid Babylon." Chapter in H.D. Galter, Die Rolle der Astronomy in den Kulteren Mesopotamiens. Graz: 1993.

Garstang, John and O.R. Gurney. The Geography of the Hittite Empire. Occasional Publications of The British Institute of Archaeology in Ankara, no. 5. London: The British Institute of Archaeology at Ankara, 1959.

Proclus. A Commentary on the First Book of Euclid's Elements. Translated with an Introduction and Notes by Glenn R Morrow. Princeton: Princeton University Press, 1970.

Ptolemy. Ptolemy'snAlmagest. Translated and Annotated by G.J. Toomer. London: Duckworth, 1984.

Snell, Bruno. "Die Nachrichten über die Lehren des Thales und die Anfänge der griechischen Philosophie - und Literaturgeschichte." [The News about the Teachings of Thales and the Beginnings of the Greek History of Philosophy and Literature], Philologus 96 (1944): 170-182.

Steele, John M."Eclipse Prediction in Mesopotamia." Archive for History of Exact Science 54 (5) (2000):421-454.

Stephenson, F. Richard, and L.V. Morrison. "Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990." Philosophical Transactions of the Royal Society of London351 (1995): 165-202.

Aristotle, An. Post., Analytica Posteriora; Cael., De Caelo; De An., De Anima; Gen An., De Generatione Animalium; Hist. An., Historia Animalium; Metaph., Metaphysics; Pol., Politics; Hist. An.; Historia Animalium

DK, Diels, Hermann and Walther Kranz.Die Fragmente der Vorsokratiker. Zurich: Weidmann, 1985.

Plutarch,Plut. De Is. et Os., De Iside et Osiride; De Pyth. or., De Pythiae oraculis; Conv. sept. sap., Convivium septem sapientium, [The Dinner of the Seven Wise Men];; Vit. Sol., Vitae Parallelae, Solon

INDETERMINATE Eternal, Infinite, Moving, Revolving (where heat differentiates from cold)

Heat on Cold produces evaporation. The sea is constantly evaporating , so one day it’ll get dry.

The sea must have covered larger extension of land. The presence of shells and sea fossils above the sea level proves it.

Evolutionary Theory: Life comes from the sea, as sea animals emerged because of evaporation. Once on earth, animals changed shape from fish to man.

ANAXIMANDER

Anaximander was the author of the first surviving lines of western philosophy. He speculated and argued about 'the Boundless' as the origin of all that is. He also worked on the fields of what we now call geography and biology. Moreover, Anaximander was the first speculative astronomer. He originated the world-picture of the open universe, which replaced the closed universe of the celestial vault.

Table of Contents (Clicking on the links below will take you to that part of this article)

The history of written Greek philosophy starts with Anaximander of Miletus in Asia Minor, a fellow-citizen of Thales. He was the first who dared to write a treatise in prose, which has been called traditionally On Nature. This book has been lost, although it probably was available in the library of the Lyceum at the times of Aristotle and his successor Theophrastus. It is said that Apollodorus, in the second century BCE, stumbled upon a copy of it, perhaps in the famous library of Alexandria. Recently, evidence has appeared that it was part of the collection of the library of Taormina in Sicily, where a fragment of a catalogue has been found, on whichAnaximander's name can be read. Only one fragment of the book has come down to us, quoted by Simplicius (after Theophrastus), in the sixth century AD. It is perhaps the most famous and most discussed phrase in the history of philosophy.

We also know very little of Anaximander's life. He is said to have led a mission that founded a colony called Apollonia on the coast of the Black Sea. He also probably introduced the gnomon (a perpendicular sun-dial) into Greece and erected one in Sparta. So he seems to have been a much-traveled man, which is not astonishing, as the Milesians were known to be audacious sailors. It is also reported that he displayed solemn manners and wore pompous garments. Most of the information on Anaximander comes from Aristotle and his pupil Theophrastus, whose book on the history of philosophy was used, excerpted, and quoted by many other authors, the so-called doxographers, before it was lost. Sometimes, in these texts words or expressions appear that can with some certainty be ascribed to Anaximander himself. Relatively many testimonies, approximately one third of them, have to do with astronomical and cosmological questions. Hermann Diels and Walter Kranz have edited the doxography (A) and the existing texts (B) of the Presocratic philosophers in Die Fragmente der Vorsokratiker, Berlin 1951-1952⁶. (A quotation like "DK 12A17" means: "Diels/Kranz, Anaximander, doxographical report no.17".)

According to Aristotle and Theophrastus, the first Greek philosophers were looking for the 'origin' or 'principle' (the Greek word 'archê' has both meanings) of all things. Anaximander is said to have identified it with 'the Boundless' or 'the Unlimited' (Greek: 'apeiron', i.e. 'that which has no boundaries'). Already in ancient times, it is complained that Anaximander did not explain what he meant by 'the Boundless'. More recently, authors have disputed whether the Boundless should be interpreted as spatially or temporarily without limits, or perhaps as that which has no qualifications, or as that which is inexhaustible. Some scholars have even defended the meaning 'that which is not experienced', by relating the Greek word 'apeiron' not to 'peras' ('boundary', 'limit'), but to 'perao' ('to experience', 'to apperceive'). The suggestion, however, is almost irresistible that Greek philosophy, by making the Boundless into the principle of all things, has started on a high level of abstraction. On the other hand, some have pointed out that this use of 'apeiron' is atypical for Greek thought, which was occupied with limit, symmetry and harmony. The Pythagoreans placed the boundless (the 'apeiron') on the list of negative things, and for Aristotle, too, perfection became aligned with limit (Greek: 'peras'), and thus 'apeiron' with imperfection. Therefore, some authors suspect eastern (Iranian) influence on Anaximander's ideas.

It seems that Anaximander not only put forward the thesis that the Boundless is the principle, but also tried to argue for it. We might say that he was the first who made use of philosophical arguments. Anaximander's arguments have come down to us in the disguise of Aristotelian jargon. Therefore, any reconstruction of the arguments used by the Milesian must remain conjectural. Verbatim reconstruction is of course impossible. Nevertheless, the data, provided they are handled with care, allow us to catch glimpses of what the arguments of Anaximander must have looked like. The important thing is, however, that he did not just utter apodictic statements, but also tried to give arguments. This is what makes him the first philosopher.

Aristotle reports a curious argument, which probably goes back to Anaximander, in which it is argued that the Boundless has no origin, because it is itself the origin. We would say that it looks more like a string of associations and word-plays than like a formal argument. It runs as follows: "Everything has an origin or is an origin. The Boundless has no origin. For then it would have a limit. Moreover, it is both unborn and immortal, being a kind of origin. For that which has become has also, necessarily, an end, and there is a termination to every process of destruction" (Physics 203b6-10, DK 12A15). The Greeks were familiar with the idea of the immortal Homeric gods. Anaximander added two distinctive features to the concept of divinity: his Boundless is an impersonal something (or 'nature', the Greek word is 'phusis'), and it is not only immortal but also unborn. However, perhaps not Anaximander, but Thales should be credited with this new idea. Diogenes Laërtius ascribes to Thales the aphorism: "What is the divine? That which has no origin and no end" (DK 11A1 (36)). Similar arguments, within different contexts, are used by Melissus (DK 30B2[9]) and Plato (Phaedrus 245d1-6).

Several sources give another argument which is somehow the other way round and answers the question of why the origin should be boundless. In Aristotle's version, it runs like this: "(The belief that there is something Boundless stems from) the idea that only then genesis and decay will never stop, when that from which is taken what has been generated, is boundless" (Physics 203b18-20, DK 12A15, other versions in DK12A14 and 12A17). In this argument, the Boundless seems to be associated with an inexhaustible source. Obviously, it is taken for granted that "genesis and decay will never stop", and the Boundless has to guarantee the ongoing of the process, like an ever-floating fountain.

A third argument is relatively long and somewhat strange. It turns on one key word (in Greek: 'êdê'), which is here translated with 'long since'. It is reproduced by Aristotle: "Some make this (viz. that which is additional to the elements) the Boundless, but not air or water, lest the others should be destroyed by one of them, being boundless; for they are opposite to one another (the air, for instance, is cold, the water wet, and the fire hot). If any of them should be boundless, it would long since have destroyed the others; but now there is, they say, something other from which they are all generated" (Physics 204b25-29, DK 12A16).

This is not only virtually the same argument as used by Plato in his Phaedo (72a12-b5), but even more interesting is that it was used almost 2500 years later by Friedrich Nietzsche in his attempts to prove his thesis of the Eternal Recurrence: "If the world had a goal, it would have been reached. If there were for it some unintended final state, this also must have been reached. If it were at all capable of a pausing and becoming fixed, if it were capable of 'being', if in the whole course of its becoming it possessed even for a moment this capability of 'being', then again all becoming would long since have come to an end." Nietzsche wrote these words in his notebook in 1885, but already in Die Philosophie im tragischen Zeitalter der Griechen (1873), which was not published during his lifetime, he mentioned the argument and credited Anaximander with it.

The only existing fragment of Anaximander's book (DK 12B1) is surrounded by all kinds of questions. The ancient Greeks did not use quotation marks, so that we cannot be sure where Simplicius, who has handed down the text to us, is still paraphrasing Anaximander and where he begins to quote him. The text is cast in indirect speech, even the part which most authors agree is a real quotation. One important word of the text ('allêlois', here translated by 'upon one another') is missing in some manuscripts. As regards the interpretation of the fragment, it is heavily disputed whether it means to refer to Anaximander's principle, the Boundless, or not. The Greek original has relative pronouns in the plural (here rendered by 'whence' and 'thence'), which makes it difficult to relate them to the Boundless. However, Simplicius' impression that it is written in rather poetic words has been repeated in several ways by many authors. Therefore, we offer a translation, in which some poetic features of the original, such as chiasmus and alliteration have been imitated:

Whence things have their origin,
Thence also their destruction happens,
As is the order of things;
For they execute the sentence upon one another
- The condemnation for the crime -
In conformity with the ordinance of Time.

In the fourth and fifth line a more fluent translation is given for what is usually rendered rather cryptic by something like "giving justice and reparation to one another for their injustice."

We may distinguish roughly two lines of interpretation, which may be labeled the 'horizontal' and the 'vertical'. The horizontal interpretation holds that in the fragment nothing is said about the relation of the things to the Boundless, whereas the vertical interpretation maintains that the fragment describes the relationship of the things to the Boundless. The upholders of the horizontal interpretation usually do not deny that Anaximander taught that all things are generated from the Boundless, but they simply hold that this is not what is said in the fragment. They argue that the fragment describes the battle between the elements (or of things in general), which accounts for the origin and destruction of things. The most obvious difficulty, however, for this 'horizontal' interpretation is that it implies two cycles of becoming and decay: one from and into the Boundless, and the other caused by the mutual give and take of the elements or things in general. In other words, in the 'horizontal' interpretation the Boundless is superfluous. This is the strongest argument in favor of the 'vertical' interpretation, which holds that the fragment refers to the Boundless, notwithstanding the plural relative pronouns. According to the 'vertical' interpretation, then, the Boundless should be regarded not only as the ever-flowing fountain from which everything ultimately springs, but also as the yawning abyss (as some say, comparable with Hesiod's 'Chaos') into which everything ultimately perishes.

The suggestion has been raised that Anaximander's formula in the first two lines of the fragment should have been the model for Aristotle's definition of the 'principle' (Greek: 'archê') of all things in Metaphysics 983b8. There is some sense in this suggestion. For what could be more natural for Aristotle than to borrow his definition of the notion of 'archê', which he uses to indicate the principle of the first presocratic philosophers, from Anaximander, the one who introduced the notion?

It is certainly important that we possess one text from Anaximander's book. On the other hand, we must recognize that we know hardly anything of its original context, as the rest of the book has been lost. We do not know from which part of his book it is, nor whether it is a text the author himself thought crucial or just a line that caught one reader's attention as an example of Anaximander's poetic writing style. The danger exists that we are tempted to use this stray text - beautiful and mysterious as it is - in order to produce all kinds of profound interpretations that are hard to verify. Perhaps a better way of understanding what Anaximander has to say is to study carefully the doxography, which goes back to people like Aristotle and Theophrastus, who probably have had Anaximander's book before their eyes, and who tried to reformulate what they thought were its central claims.

The Boundless seems to have played a role in Anaximander's account of the origin of the cosmos. Its eternal movement is said to have caused the origin of the heavens. Elsewhere, it is said that "all the heavens and the worlds within them" have sprung from "some boundless nature". A part of this process is described in rather poetic language, full of images, which seems to be idiosyncratic for Anaximander: "a germ, pregnant with hot and cold, was separated [or: separated itself] off from the eternal, whereupon out of this germ a sphere of fire grew around the vapor that surrounds the earth, like a bark round a tree" (DK 12A10). Subsequently, the sphere of fire is said to have fallen apart into several rings, and this event was the origin of sun, moon, and stars. There are authors who have, quite anachronistically, seen here a kind of foreshadowing of the Kant-Laplace theory of the origin of the solar system. Some sources even mention innumerable worlds (in time and/or in space), which looks like a plausible consequence of the Boundless as principle. But this is presumably a later theory, incorrectly read back into Anaximander.

At first sight, the reports on Anaximander's astronomy look rather bizarre and obscure. Some authors even think that they are so confused that we should give up trying to offer a satisfying and coherent interpretation. The only way of understanding Anaximander's astronomical ideas, however, is to take them seriously and treat them as such, that is, as astronomical ideas. It will appear that many of the features of his universe that look strange at first sight make perfect sense on closer inspection.

The astronomy of neighboring peoples, such as the Babylonians and the Egyptians, consists mainly of observations of the rising and disappearance of celestial bodies and of their paths across the celestial vault. These observations were made with the naked eye and with the help of some simple instruments as the gnomon. The Babylonians, in particular, were rather advanced observers. Archeologists have found an abundance of cuneiform texts on astronomical observations. In contrast, there exists only one report of an observation made by Anaximander, which concerns the date on which the Pleiades set in the morning. This is no coincidence, for Anaximander's merits do not lie in the field of observational astronomy, unlike the Babylonians and the Egyptians, but in that of speculative astronomy. We may discern three of his astronomical speculations: (1) that the celestial bodies make full circles and pass also beneath the earth, (2) that the earth floats free and unsupported in space, and (3) that the celestial bodies lie behind one another. Notwithstanding their rather primitive outlook, these three propositions, which make up the core of Anaximander's astronomy, meant a tremendous jump forward and constitute the origin of our western concept of the universe.

The idea that the celestial bodies, in their daily course, make full circles and thus pass also beneath the earth - from Anaximander's viewpoint - is so self-evident to us that it is hard to understand how daring its introduction was. That the celestial bodies make full circles is not something he could have observed, but a conclusion he must have drawn. We would say that this is a conclusion that lies to hand. We can see - at the northern hemisphere, like Anaximander - the stars around the Polar star making full circles, and we can also observe that the more southerly stars sometimes disappear behind the horizon. We may argue that the stars of which we see only arcs in reality also describe full circles, just like those near the Polar star. As regards the sun and moon, we can observe that the arcs they describe are sometimes bigger and sometimes smaller, and we are able to predict exactly where they will rise the next day. Therefore, it seems not too bold a conjecture to say that these celestial bodies also describe full circles. Nevertheless, it was a daring conclusion, precisely because it necessarily entailed the concept of the earth hanging free and unsupported in space.

Anaximander boldly asserts that the earth floats free in the center of the universe, unsupported by water, pillars, or whatever. This idea means a complete revolution in our understanding of the universe. Obviously, the earth hanging free in space is not something Anaximander could have observed. Apparently, he drew this bold conclusion from his assumption that the celestial bodies make full circles. More than 2500 years later astronauts really saw the unsupported earth floating in space and thus provided the ultimate confirmation of Anaximander's conception. The shape of the earth, according to Anaximander, is cylindrical, like a column-drum, its diameter being three times its height. We live on top of it. Some scholars have wondered why Anaximander chose this strange shape. The strangeness disappears, however, when we realize that Anaximander thought that the earth was flat and circular, as suggested by the horizon. For one who thinks, as Anaximander did, that the earth floats unsupported in the center of the universe, the cylinder-shape lies at hand.

We may assume that Anaximander somehow had to defend his bold theory of the free-floating, unsupported earth against the obvious question of why the earth does not fall. Aristotle's version of Anaximander's argument runs like this: "But there are some who say that it (viz. the earth) stays where it is because of equality, such as among the ancients Anaximander. For that which is situated in the center and at equal distances from the extremes, has no inclination whatsoever to move up rather than down or sideways; and since it is impossible to move in opposite directions at the same time, it necessarily stays where it is." (De caelo 295b10ff., DK 12A26) Many authors have pointed to the fact that this is the first known example of an argument that is based on the principle of sufficient reason (the principle that for everything which occurs there is a reason or explanation for why it occurs, and why this way rather than that).

Anaximander's argument returns in a famous text in the Phaedo (108E4 ff.), where Plato, for the first time in history, tries to express the sphericity of the earth. Even more interesting is that the same argument, within a different context, returns with the great protagonist of the principle of sufficient reason, Leibniz. In his second letter to Clarke, he uses an example, which he ascribes to Archimedes but which reminds us strongly of Anaximander: "And therefore Archimedes (...) in his book De aequilibrio, was obliged to make use of a particular case of the great Principle of a sufficient reason. He takes it for granted that if there be a balance in which everything is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will stay at rest. This is because there is no reason why one side should weigh down, rather than the other".

One may doubt, however, whether the argument is not fallacious. Aristotle already thought the argument to be deceiving. He ridicules it by saying that according to the same kind of argument a hair, which was subject to an even pulling power from opposing sides, would not break, and that a man, being just as hungry as thirsty, placed in between food and drink, must necessarily remain where he is and starve. To him it was the wrong argument for the right proposition. Absolute propositions concerning the non-existence of things are always in danger of becoming falsified on closer investigation. They contain a kind of subjective aspect: 'as far as I know'. Several authors, however, have said that Anaximander's argument is clear and ingenious. Already at first sight this qualification sounds strange, for the argument evidently must be wrong, as the earth is not in the center of the universe, although it certainly is not supported by anything but gravity. Nevertheless, we have to wait until Newton for a better answer to the question why the earth does not fall.

When Anaximander looked at the heaven, he imagined, for the first time in history, space. Anaximander's vision implied depth in the universe, that is, the idea that the celestial bodies lie behind one another. Although it sounds simple, this is a remarkable idea, because it cannot be based on direct observation. We do not see depth in the universe. The more natural and primitive idea is that of the celestial vault, a kind of dome or tent, onto which the celestial bodies are attached, all of them at the same distance, like in a planetarium. One meets this kind of conception in Homer, when he speaks of the brazen or iron heaven, which is apparently conceived of as something solid, being supported by Atlas, or by pillars.

Anaximander placed the celestial bodies in the wrong order. He thought that the stars were nearest to the earth, then followed the moon, and the sun farthest away. Some authors have wondered why Anaximander made the stars the nearest celestial bodies, for he should have noticed the occurrence of star-occultations by the moon. This is a typical anachronism, which shows that it not easy to look at the phenomena with Anaximander's eyes. Nowadays, we know that the stars are behind the moon, and thus we speak of star-occultation when we see a star disappear behind the moon. But Anaximander had no reason at all, from his point of view, to speak of a star-occultation when he saw a star disappear when the moon was at the same place. So it is a petitio principii to say that for him occultations of stars were easy to observe. Perhaps he observed stars disappearing and appearing again, but he did not observe - could not see it as - the occultation of the star, for that interpretation did not fit his paradigm. The easiest way to understand his way of looking at it - if he observed the phenomenon at all - is that he must have thought that the brighter light of the moon outshines the much smaller light of the star for a while. Anaximander's order of the celestial bodies is clearly that of increasing brightness. Unfortunately, the sources do not give further information of his considerations at this point.

A peculiar feature of Anaximander's astronomy is that the celestial bodies are said to be like chariot wheels (the Greek words for this image are presumably his own). The rims of these wheels are of opaque vapor, they are hollow, and filled with fire. This fire shines through at openings in the wheels, and this is what we see as the sun, the moon, or the stars. Sometimes, the opening of the sun wheel closes: then we observe an eclipse. The opening of the moon wheel regularly closes and opens again, which accounts for the phases of the moon. This image of the celestial bodies as huge wheels seems strange at first sight, but there is a good reason for it. There is no doxographic evidence of it, but it is quite certain that the question of why the celestial bodies do not fall upon the earth must have been as serious a problem to Anaximander as the question of why the earth does not fall. The explanation of the celestial bodies as wheels, then, provides an answer to both questions. The celestial bodies have no reason whatsoever to move otherwise than in circles around the earth, as each point on them is always as far from the earth as any other. It is because of reasons like this that for ages to come, when Anaximander's concept of the universe had been replaced by a spherical one, the celestial bodies were thought of as somehow attached to crystalline or ethereal sphere-shells, and not as free-floating bodies.

Many authors, following Diels, make the image of the celestial wheels more difficult than is necessary. They say that the light of a celestial bodies shines through the openings of its wheel 'as through the nozzle of a bellows'. This is an incorrect translation of an expression that probably goes back to Anaximander himself. The image of a bellows, somehow connected to a celestial wheel, tends to complicate rather than elucidate the meaning of the text. If we were to understand that every celestial body had such a bellows, the result would be hundreds of nozzles (or pipes), extending from the celestial wheels towards the earth. Anaximander's intention, however, can be better understood not as an image, but as a comparison of the light of the celestial bodies with that of lightning. Lightning, according to Anaximander, is a momentary flash of light against a dark cloud. The light of a celestial body is like a permanent beam of lightning fire that originates from the opaque cloudy substance of the celestial wheel.

The doxography gives us some figures about the dimensions of Anaximander's universe: the sun wheel is 27 or 28 times the earth, and the moon wheel is 19 times the earth. More than a century ago, two great scholars, Paul Tannery and Hermann Diels, solved the problem of Anaximander's numbers. They suggested that the celestial wheels were one unit thick, this unit being the diameter of the earth. The full series, they argued, had to be: 9 and 10 for the stars, 18 and 19 for the moon, and 27 and 28 for the sun. These numbers are best understood as indicating the distances of the celestial bodies to the earth. In others words, they indicate the radii of concentric circles, made by the celestial wheels, with the earth as the center. See Figure 1, a plane view of Anaximander's universe.

These numbers cannot be based on observation. In order to understand their meaning, we have to look at Hesiod's Theogony 722-725, where it is said that a brazen anvil would take nine days to fall from heaven to earth before it arrives on the tenth day. It is not a bold guess to suppose that Anaximander knew this text. The agreement with his numbers is too close to neglect, for the numbers 9 and 10 are exactly those extrapolated for Anaximander's star wheel. Hesiod can be seen as a forerunner to Anaximander, for he tried to imagine the distance to the heaven. In the Greek counting system Hesiod's numbers should be taken to mean 'a very long time'. Thus, Troy was conquered in the tenth year after having stood the siege for nine years; and Odysseus scoured the seas for nine years before reaching his homeland in the tenth year. We may infer that Anaximander, with his number 9 (1 x 3 x 3) for the star ring, simply was trying to say that the stars are very far away. Now the numbers 18 and 27 can easily be interpreted as 'farther' (2 x 3 x 3, for the moon ring) and 'farthest' (3 x 3 x 3, for the sun ring). And this is exactly what we should expect one to say, who had discovered that the image of the celestial vault was wrong but that the celestial bodies were behind one another, and who wished to share this new knowledge with his fellow citizens in a language they were able to understand.

Although it is not attested in the doxography, we may assume that Anaximander himself drew a map of the universe, like that in figure 1. The numbers, 9, 10, 18, etc., can easily be understood as instructions for making such a map. Although Diogenes Laërtius reports that he made a 'sphere', the drawing or construction of a three-dimensional model must be considered to have been beyond Anaximander's abilities. On the other hand, it is quite easy to explain the movements of the celestial bodies with the help of a plan view, by making broad gestures, describing circles in the air, and indicating direction, speed, and inclination with your hands, as is said of a quarrel between Anaxagoras and Oenopides (DK 41A2).

Almost nothing of Anaximander's opinions about the stars has been handed down to us. Probably the best way to imagine them is as a conglomerate of several wheels, each of which has one or more holes, through which the inner fire shines, which we see as stars. The most likely sum-total of these star wheels is a sphere. The only movement of these star wheels is a rotation around the earth from east to west, always at the same speed, and always at the same place relative to one another in the heaven. The sun wheel shows the same rotation from east to west as the stars, but there are two differences. The first is that the speed of the rotation of the sun wheel is not the same as that of the stars. We can see this phenomenon by observing how the sun lags behind by approximately one degree per day. The second difference is that the sun wheel as a whole changes its position in the heaven. In summer it moves towards the north along the axis of the heaven and we see a large part of it above the horizon, whereas in winter we only observe a small part of the sun wheel, as it moves towards the south. This movement of the sun wheel accounts for the seasons. The same holds mutatis mutandis for the moon. Today, we use to describe this movement of the sun (and mutatis mutandis of the moon and the planets) as a retrograde movement, from west to east, which is a counter-movement to the daily rotation from east to west. In terms of Anaximander's ancient astronomy it is more appropriate and less anachronistic to describe it as a slower movement of the sun wheel from east to west. The result is that we see different stars in different seasons, until the sun, at the end of a year, reaches its old position between the stars.

Due to the inclination of the axis of the heaven, the celestial bodies do not circle around the earth in the same plane as the earth's - flat - surface, but are tilted. This inclination amounts to about 38.5 degrees when measured at Delphi, the world's navel. The earth being flat, the inclination must be the same all over its surface. This tilting of the heaven's axis must have been one of the biggest riddles of the universe. Why is it tilted at all? Who or what is responsible for this phenomenon? And why is it tilted just the way it is? Unfortunately, the doxography on Anaximander has nothing to tell us about this problem. Later, other Presocratics like Empedocles, Diogenes of Apollonia, and Anaxagoras discuss the tilting of the heavens.

Although there exists a report that says the contrary, it is not likely that Anaximander was acquainted with the obliquity of the ecliptic, which is the yearly path of the sun along the stars. The ecliptic is a concept which belongs to the doctrine of a spherical earth within a spherical universe. A three-dimensional representation of Anaximander's universe is given in Figures 2 and 3.

Anaximander is said to have made the first map of the world. Although this map has been lost, we can imagine what it must have looked like, because Herodotus, who has seen such old maps, describes them. Anaximander's map must have been circular, like the top of his drum-shaped earth. The river Ocean surrounded it. The Mediterranean Sea was in the middle of the map, which was divided into two halves by a line that ran through Delphi, the world's navel. The northern half was called 'Europe', the southern half 'Asia'. The habitable world (Greek: 'oikoumenê') consisted of two relatively small strips of land to the north and south of the Mediterranean Sea (containing Spain, Italy, Greece, and Asia Minor on the one side, and Egypt and Libya on the other side), together with the lands to the east of the Mediterranean Sea: Palestine, Assyria, Persia, and Arabia. The lands to the north of this small 'habitable world' were the cold countries where mythical people lived. The lands to the south of it were the hot countries of the black burnt people.

The doxography tells us that according to Anaximander life originated from the moisture that covered the earth before it was dried up by the sun. The first animals were a kind of fish, with a thorny skin (the Greek word is the same that was used for the metaphor 'the bark of a tree' in Anaximander's cosmology). Originally, men were generated from fishes and were fed in the manner of a viviparous shark. The reason for this is said to be that the human child needs long protection in order to survive. Some authors have, rather anachronistically, seen in these scattered statements a proto-evolutionist theory.

It is no use trying to unify the information on Anaximander into one all-compassing and consistent whole. His work will always remain truncated, like the mutilated and decapitated statue that has been found at the market-place of Miletus and that bears his name. Nevertheless, by what we know of him, we may say that he was one of the greatest minds that ever lived. By speculating and arguing about the 'Boundless' he was the first metaphysician. By drawing a map of the world he was the first geographer. But above all, by boldly speculating about the universe he broke with the ancient image of the celestial vault and became the discoverer of the western world-picture.

Diels, H. and W. Kranz, Die Fragmente der Vorsokratiker. Zürich/Hildesheim 1964

The standard collection of the texts of and the doxography on Anaximander and the other presocratics.

Guthrie, W.K.C. A History of Greek Philosophy I, The Earlier Presocratics and the Pythagoreans. London/New York 1985 (Cambridge 1962)

Kirk, G.S., J.E. Raven, and M. Schofield, The Presocratic Philosophers, Cambridge 1995 (1957)

The above two works each have a good survey of Anaximander's thoughts in the context of ancient Greek philosophy, with translations of the most important doxography.

Kahn, C.H. Anaximander and the Origins of Greek Cosmology. New York 1960 (Indianapolis/Cambridge 1994)

A classical study on Anaximander's cosmology and his fragment, also with many translations.

Furley, D.J. and R.E. Allen, eds. Studies in Presocratic Philosophy, Vol. I, The Beginnings of Philosophy. New York/London 1970

Couprie, D.L., R. Hahn, and G. Naddaf, Anaximander in Context. Albany 2002 (forthcoming)

Kahn, C.H. "Anaximander and the Arguments Concerning the Apeiron at Physics 203b4-1". in: Festschrift E. Kapp, Hamburg 1958, pp.19-29.

Stokes, M.C. "Anaximander's Argument". in: R.A. Shiner & J. King-Farlow, eds., New Essays on Plato and the Presocratics. 1976, pp.1-22.

Dicks, D.R. "Solstices, Equinoxes, and the Presocratics", The Journal of Hellenic Studies 86. 1966, pp.26-40

Kahn, C.H. "On Early Greek Astronomy". The Journal of Hellenic Studies 90. 1970, pp.99-116

Bodnár, I.M. "Anaximander's Rings", Classical Quarterly 38. 1988, pp. 49-51

O'Brien, D. "Anaximander's Measurements", The Classical Quarterly 17. 1967, pp.423-432

McKirahan, R. "Anaximander's Infinite Worlds", in A. Preus, ed., Essays in Ancient Greek Philosophy VI: Before Plato, Albany 2001, pp. 49-65

Heidel, W.A. The Frame of the Ancient Greek Maps. With a Discussion of the Discovery of the Sphericity of the Earth. New York 1937

Loenen, J.H.M.M. "Was Anaximander an Evolutionist?" Mnemosyme 4. 1954, pp.215-232

Classen, C.J. Ansätze. Beiträge zum Verständnis der frühgriechischen Philosophie. Würzburg/Amsterdam 1986

Anaximenes was the third Greek philosopher in canonical lists of successions, and like his predecessors Thales and Anaximander, an inhabitant of Miletus. According to the very meager sources on his life he flourished in the mid 6th century BCE and died around 528. He was said to be the student of Anaximander, and like him he sought to give a quasi-scientific explanation of the world.

He is best known for his doctrine that air is the source of all things. This claim contrasts with the view of Thales that water was the source, and with the view of Anaximander that all things came from an unspecified boundless stuff. He seems to have held that at one time everything was air. In one region the air was acted upon by natural forces to be transformed into other materials which came together into an organized world, in which we now live. Air can be thought of as a kind of neutral stuff that is found everywhere, and is hence available to participate in physical processes. It is also associated with the soul-sometimes portrayed as the breath of life in early Greek literature-and hence with life and intelligence. Anaximenes may have thought of air as capable of directing its own development to some extent as our soul controls our body (DK13B2 in the Diels-Kranz collection of Presocratic sources). Accordingly, he ascribed to air divine attributes.

[Air] differs in essence in accordance with its rarity or density. When it is thinned it becomes fire, while when it is condensed it becomes wind, then cloud, when still more condensed it becomes water, then earth, then stones. Everything else comes from these. (DK13A5)

Using two contrary processes of rarefaction and condensation, Anaximenes explains how air is part of a series of changes from fire to air to wind to cloud to water to earth to stones. Matter can travel this path by being condensed, or the reverse path from stones to fire by being successively more rarefied. Anaximenes provides a crude kind of empirical support by appealing to a simple experiment: if one blows on one's hand with the mouth relaxed, the air is hot; if one blows with pursed lips, the air is cold (DK13B1). Hence, we allegedly see that rarity is correlated with heat, as in fire, density with coldness, as in the denser stuffs. Anaximenes is the first thinker we know of who provides a theory of change and bolsters it with observations. Anaximander had described a sequence of changes that a portion of the boundless underwent to form the different stuffs of the world. But he gave no scientific reason for its changing, nor did he describe any mechanism by which it might come about. By contrast, Anaximenes uses a process familiar from everyday experience to account for material change. He also seems to have referred to the process of felting, by which wool is compressed to make felt. This industrial process provides a model of how one stuff can take on new properties when it is compacted.

Anaximenes, like Anaximander, gives an account of how our world came to be out of previously existing matter. According to Anaximenes earth was formed from air by a felting process. It is a flat disk. From evaporations from the earth fiery bodies arise which come to be the heavenly bodies. The earth floats on a cushion of air. The heavenly bodies, or at least the sun and the moon, seem also be flat bodies that float on streams of air. On one account the heaven is like a felt cap that turns around the head. The stars may be fixed to this surface like nails. In another account the stars are like fiery leaves floating on air (DK13A14). The sun does not travel under the earth but circles around it, and is hidden by the higher parts of the earth at night.

Like Anaximander, Anaximenes uses his principles to account for various natural phenomena. Lightning and thunder result from wind breaking out of clouds; rainbows are the result of the rays of the sun falling on clouds; earthquakes are caused by the cracking of the earth when it dries out after being moistened by rains. He gives an essentially correct account of hail as frozen rainwater.

Most commentators, following Aristotle, understand Anaximenes' theory of change as presupposing Material Monism. According to this theory there is only one substance, in this case air, from which the whole world and everything in it are composed. The several stuffs: wind, cloud, water, etc., are only modifications of the real substance that is always and everywhere present. There is no independent evidence to support this interpretation, which seems to require metaphysical concepts of form and matter, substratum and accident that are too advanced for this period. Anaximenes may have supposed that the stuffs simply change into one another in order.

Anaximenes' notion of successive change of matter by rarefaction and condensation was influential in later theories. It is developed by Heraclitus (DK22B31) and criticized by Parmenides (DK28B8.23-24, 47-48). His general theory of how the materials of the world arise is adopted by Anaxagoras (DK59B16), even though the latter has a very different theory of matter. Both Melissus (DK30B8.3) and Plato (Timaeus 49b-c) see Anaximenes' theory as providing a common-sense explanation of change. Diogenes of Apollonia makes air the basis of his explicitly monistic theory. The Hippocratic treatise On Breaths uses air as the central concept in a theory of diseases. By providing cosmological accounts with a theory of change Anaximenes removed them from the realm of mere speculation and made them, at least in conception, scientific theories capable of testing.

There are no monographs on Anaximenes in English. Articles on him are sometimes rather specialized in nature. A number of chapters in books on the Presocratics are helpful.

Barnes, Jonathan. The Presocratic Philosophers. London: Routledge & Kegan Paul (1 vol. edn.), 1982. Ch. 3.

Gives a philosophically rich defense of the standard interpretation of Anaximenes.

An interesting reconstruction of the conflicting reports on Anaximenes' astronomy.

Classen, C. Joachim. "Anaximander and Anaximenes: The Earliest Greek Theories of Change?" Phronesis 22: 89-102.

This article provides a good assessment of one of Anaximenes' major contributions.

Guthrie, W. K. C. A History of Greek Philosophy. Vol. 1. Cambridge: Cambridge U. Pr., 1962. 115-40.

Kirk, G. S., J. E. Raven and M. Schofield. The Presocratic Philosophers. 2nd edn. Cambridge: Cambridge UP, 1983. Ch. 4.

Wöhrle, Georg. Anaximenes aus Milet. Stuttgart: Franz Steiner Verlag, 1993.

This brief edition adds four new testimonies to the evidence about Anaximenes and challenges the standard interpretation. It is useful as a counterbalance to the received view, though I think particular criticisms it makes of that view are wrong.

1) Separated senses from reason, as a) to perceive is not to understand; b) to understand we take what we perceive and submit it to reason (We don’t see rarefaction, condensation, indeterminacy).

A Greek philosopher of the late 6th century BCE, Heraclitus criticizes his predecessors and contemporaries for their failure to see the unity in experience. He claims to announce an everlasting Word (Logos) according to which all things are one, in some sense. Opposites are necessary for life, but they are unified in a system of balanced exchanges. The world itself consists of a law-like interchange of elements, symbolized by fire. Thus the world is not to be identified with any particular substance, but rather with an ongoing process governed by a law of change. The underlying law of nature also manifests itself as a moral law for human beings. Heraclitus is the first Western philosopher to go beyond physical theory in search of metaphysical foundations and moral applications.

Table of Contents (Clicking on the links below will take you to that part of this article)

Heraclitus lived in Ephesus, an important city on the Ionian coast of Asia Minor, not far from Miletus, the birthplace of philosophy. We know nothing about his life other than what can be gleaned from his own statements, for all ancient biographies of him consist of nothing more than inferences or imaginary constructions based on his sayings. Although Plato thought he wrote after Parmenides, it is more likely he wrote before Parmenides. For he criticizes by name important thinkers and writers with whom he disagrees, and he does not mention Parmenides. On the other hand, Parmenides in his poem arguably echoes the words of Heraclitus. Heraclitus criticizes the mythographers Homer and Hesiod, as well as the philosophers Pythagoras and Xenophanes and the historian Hecataeus. All of these figures flourished in the 6th century BCE or earlier, suggesting a date for Heraclitus in the late 6th century. Although he does not speak in detail of his political views in the extant fragments, Heraclitus seems to reflect an aristocratic disdain for the masses and favor the rule of a few wise men, for instance when he recommends that his fellow-citizens hang themselves because they have banished their most prominent leader (DK22B121 in the Diels-Kranz collection of Presocratic sources).

Heraclitus sees the great majority of human beings as lacking understanding:

Of this Word's being forever do men prove to be uncomprehending, both before they hear and once they have heard it. For although all things happen according to this Word they are like the unexperienced experiencing words and deeds such as I explain when I distinguish each thing according to its nature and declare how it is. Other men are unaware of what they do when they are awake just as they are forgetful of what they do when they are asleep. (DK22B1)

Most people sleep-walk through life, not understanding what is going on about them. Yet experience of words and deeds can enlighten those who are receptive to their meaning. (The opening sentence is ambiguous: does the 'forever' go with the preceding or the following words? Heraclitus prefigures the semantic complexity of his message.)

On the one hand, Heraclitus commends sense experience: "The things of which there is sight, hearing, experience, I prefer" (DK22B55). On the other hand, "Poor witnesses for men are their eyes and ears if they have barbarian souls" (DK22B107). A barbarian is one who does not speak the Greek language. Thus while sense experience seems necessary for understanding, if we do not know the right language, we cannot interpret the information the senses provide. Heraclitus does not give a detailed and systematic account of the respective roles of experience and reason in knowledge. But we can learn something from his manner of expression.

Describing the practice of religious prophets, Heraclitus says, "The Lord whose oracle is at Delphi neither reveals nor conceals, but gives a sign" (DK22B93). Similarly, Heraclitus does not reveal or conceal, but produces complex expressions that have encoded in them multiple messages for those who can interpret them. He uses puns, paradoxes, antitheses, parallels, and various rhetorical and literary devices to construct expressions that have meanings beyond the obvious. This practice, together with his emphasis on the Word (Logos) as an ordering principle of the world, suggests that he sees his own expressions as imitations of the world with its structural and semantic complexity. To read Heraclitus the reader must solve verbal puzzles, and to learn to solve these puzzles is to learn to read the signs of the world. Heraclitus stresses the inductive rather than the deductive method of grasping the world, a world that is rationally structured, if we can but discern its shape.

For those who can discern it, the Word has an overriding message to impart: "Listening not to me but to the Word it is wise to agree that all things are one" (DK22B50). It is perhaps Heraclitus's chief project to explain in what sense all things are one.

According to both Plato and Aristotle, Heraclitus held extreme views that led to logical incoherence. For he held that (1) everything is constantly changing and (2) opposite things are identical, so that (3) everything is and is not at the same time. In other words, Universal Flux and the Identity of Opposites entail a denial of the Law of Non-Contradiction. Plato indicates the source of the flux doctrine: "Heraclitus, I believe, says that all things go and nothing stays, and comparing existents to the flow of a river, he says you could not step twice into the same river" (Cratylus 402a = DK22A6).

On those stepping into rivers staying the same other and other waters flow. (DK22B12)

There is an antithesis between 'same' and 'other.' The sentence says that different waters flow in rivers staying the same. In other words, though the waters are always changing, the rivers stay the same. Indeed, it must be precisely because the waters are always changing that there are rivers at all, rather than lakes or ponds. The message is that rivers can stay the same over time even though, or indeed because, the waters change. The point, then, is not that everything is changing, but that the fact that some things change makes possible the continued existence of other things. Perhaps more generally, the change in elements or constituents supports the constancy of higher-level structures. As for the alleged doctrine of the Identity of Opposites, Heraclitus does believe in some kind of unity of opposites. For instance, "God is day night, winter summer, war peace, satiety hunger . . ." (DK22B67). But if we look closer, we see that the unity in question is not identity:

As the same thing in us is living and dead, waking and sleeping, young and old. For these things having changed around are those, and conversely those having changed around are these. (DK22B88)

The second sentence in B88 gives the explanation for the first. If F is the same as G because F turns into G, then the two are not identical. And Heraclitus insists on the common-sense truth of change: "Cold things warm up, the hot cools off, wet becomes dry, dry becomes wet" (DK22B126). This sort of mutual change presupposes the non-identity of the terms. What Heraclitus wishes to maintain is not the identity of opposites but the fact that they replace each other in a series of transformations: they are interchangeable or transformationally equivalent.

Thus, Heraclitus does not hold Universal Flux, but recognizes a lawlike flux of elements; and he does not hold the Identity of Opposites, but the Transformational Equivalence of Opposites. The views that he does hold do not, jointly or separately, entail a denial of the Law of Non-Contradiction. Heraclitus does, to be sure, make paradoxical statements, but his views are no more self-contradictory than are the paradoxical claims of Socrates. They are, presumably, meant to wake us up from our dogmatic slumbers.

Heraclitus' theory can be understood as a response to the philosophy of his Ionian predecessors. The philosophers of the city of Miletus (near Ephesus), Thales, Anaximander, and Anaximenes, believed some original material turns into all other things. The world as we know it is the orderly articulation of different stuffs produced out of the original stuff. For the Milesians, to explain the world and its phenomena was just to show how everything came from the original stuff, such as Thales' water orAnaximenes' air.

Heraclitus seems to follow this pattern of explanation when he refers to the world as "everliving fire" (DK22B30, quoted in full in next section) and makes statements such as "Thunderbolt steers all things," alluding to the directive power of fire (DK22B64). But fire is a strange stuff to make the origin of all things, for it is the most inconstant and changeable. It is, indeed, a symbol of change and process. Heraclitus observes,

All things are an exchange for fire, and fire for all things, as goods for gold and gold for goods. (DK22B90)

We can measure all things against fire as a standard; there is an equivalence between all things and gold, but all things are not identical to gold. Similarly, fire provides a standard of value for other stuffs, but it is not identical to them. Fire plays an important role in Heraclitus' system, but it is not the unique source of all things, because all stuffs are equivalent.

Ultimately, fire may be more important as a symbol than as a stuff. Fire is constantly changing-but so is every other stuff. One thing is transformed into another in a cycle of changes. What is constant is not some stuff, but the overall process of change itself. There is a constant law of transformations, which is, perhaps, to be identified with the Logos. Heraclitus may be saying that the Milesians correctly saw that one stuff turns into another in a series, but they incorrectly inferred from this that some one stuff is the source of everything else. But if A is the source of B and B of C, and C turns back into B and then A, then B is likewise the source of A and C, and C is the source of A and B. There is no particular reason to promote one stuff at the expense of the others. What is important about the stuffs is that they change into others. The one constant in the whole process is the law of change by which there is an order and sequence to the changes. If this is what Heraclitus has in mind, he goes beyond the physical theory of his early predecessors to arrive at something like a process philosophy with a sophisticated understanding of metaphysics.

Heraclitus' criticisms and metaphysical speculations are grounded in a physical theory. He expresses the principles of his cosmology in a single sentence:

This world-order, the same of all, no god nor man did create, but it ever was and is and will be: everliving fire, kindling in measures and being quenched in measures. (DK22B30)

This passage contains the earliest extant philosophical use of the word kosmos, "world-order," denoting the organized world in which we live, with earth, sea, atmosphere, and heavens. While ancient sources understand Heraclitus as saying the world comes to be and then perishes in a fiery holocaust, only to be born again (DK22A10), the present passage seems to contradict this reading: the world itself does not have a beginning or end. Parts of it are being consumed by fire at any given time, but the whole remains. Almost all other early cosmologists before and after Heraclitus explained the existence of the ordered world by recounting its origin out of elemental stuffs. Some also predicted the extinction of the world. But Heraclitus, the philosopher of flux, believes that as the stuffs turn into one another, the world itself remains stable. How can that be?

The turnings of fire: first sea, and of sea, half is earth, half firewind (prêstêr: some sort of fiery meteorological phenomenon). (DK22B31a)

Sea is liquefied and measured into the same proportion as it had before it became earth. (DK22B31b)

Fire is transformed into water ("sea") of which half turns back into fire ("firewind") and half into earth. Thus there is a sequence of stuffs: fire, water, earth, which are interconnected. When earth turns back into sea, it occupies the same volume as it had before it turned into earth. Thus we can recognize a primitive law of conservation-not precisely conservation of matter, at least the identity of the matter is not conserved, nor of mass, but at least an equivalence of matter is maintained. Although the fragments do not give detailed information about Heraclitus' physics, it seems likely that the amount of water that evaporates each day is balanced by the amount of stuff that precipitates as water, and so on, so that a balance of stuffs is maintained even though portions of stuff are constantly changing their identity.

For Heraclitus, flux and opposition are necessary for life. Aristotle reports,

Heraclitus criticizes the poet who said, 'would that strife might perish from among gods and men' [Homer Iliad 18.107]' for there would not be harmony without high and low notes, nor living things without female and male, which are opposites. (DK22A22)

We must recognize that war is common and strife is justice, and all things happen according to strife and necessity. (DK22B80)

War is the father of all and king of all, who manifested some as gods and some as men, who made some slaves and some freemen. (DK22B53)

In a tacit criticism of Anaximander, Heraclitus rejects the view that cosmic justice is designed to punish one opposite for its transgressions against another. If it were not for the constant conflict of opposites, there would be no alternations of day and night, hot and cold, summer and winter, even life and death. Indeed, if some things did not die, others would not be born. Conflict does not interfere with life, but rather is a precondition of life.

As we have seen, for Heraclitus fire changes into water and then into earth; earth changes into water and then into fire. At the level of either cosmic bodies (in which sea turns into fiery storms on the one hand and earth on the other) or domestic activities (in which, for instance, water boils out of a pot), there is constant flux among opposites. To maintain the balance of the world, we must posit an equal and opposite reaction to every change. Heraclitus observes,

Here again we find a unity of opposites, but no contradiction. One road is used to pursue two different routes. Daily traffic carries some travelers out of the city, while it brings some back in. The image applies equally to physical theory: as earth changes to fire, fire changes to earth. And it may apply to psychology and other domains as well.

There has been some debate as to whether Heraclitus is chiefly a philosopher of nature (a view championed by G. S. Kirk) or a philosopher concerned with the human condition (C. H. Kahn). The opening words of Heraclitus' book (DK22B1, quoted above) seem to indicate that he will expound the nature of things in a way that will have profound implications for human life. In other words, he seems to see the theory of nature and the human condition as intimately connected. In fact, recently discovered papyri have shown that Heraclitus is concerned with technical questions of astronomy, not only with general theory. There is no reason, then, to think of him as solely a humanist or moral philosopher. On the other hand, it would be wrong to think of him as a straightforward natural philosopher in the manner of other Ionian philosophers, for he is deeply concerned with the moral implications of physical theory.

To souls it is death to become water, to water death to become earth, but from earth water is born, and from water soul. (DK22B36)

Soul is generated out of other substances just as fire is. But it has a limitless dimension:

If you went in search of it, you would not find the boundaries of the soul, though you traveled every road-so deep is its measure [logos]. (DK22B45)

Drunkenness damages the soul by causing it to be moist, while a virtuous life keeps the soul dry and intelligent. Souls seem to be able to survive death and to fare according to their character.

The people [of a city] should fight for their laws as they would for their city wall. (DK22B44)

Speaking with sense we must rely on a common sense of all things, as a city relies on its wall, and much more reliably. For all human laws are nourished by the one divine law. For it prevails as far as it will and suffices for all and overflows. (DK22B114)

The laws provide a defense for a city and its way of life. But the laws are not merely of local interest: they derive their force from a divine law. Here we see the notion of a law of nature that informs human society as well as nature. There is a human cosmos that like the natural cosmos reflects an underlying order. The laws by which human societies are governed are not mere conventions, but are grounded in the ultimate nature of things. One cannot break a human law with impunity. The notion of a law-like order in nature has antecedents in the theory of Anaximander, and the notion of an inherent moral law influences the Stoics in the 3rd century BCE.

Heraclitus recognizes a divine unity behind the cosmos, one that is difficult to identify and perhaps impossible to separate from the processes of the cosmos:

The wise, being one thing only, would and would not take the name of Zeus [or: Life]. (DK22B32)

God is day night, winter summer, war peace, satiety hunger, and it alters just as when it is mixed with incense is named according to the aroma of each. (DK22B67)

Evidently the world either is god, or is a manifestation of the activity of god, which is somehow to be identified with the underlying order of things. God can be thought of as fire, but fire, as we have seen, is constantly changing, symbolic of transformation and process. Divinity is present in the world, but not as a conventional anthropomorphic being such as the Greeks worshiped.

Heraclitus goes beyond the natural philosophy of the other Ionian philosophers to make profound criticisms and develop far-reaching implications of those criticisms. He suggests the first metaphysical foundation for philosophical speculation, anticipating process philosophy. And he makes human values a central concern of philosophy for the first time. His aphoristic manner of expression and his manner of propounding general truths through concrete examples remained unique.

Heraclitus's paradoxical exposition may have spurred Parmenides' rejection of Ionian philosophy. Empedocles and some medical writers echoed Heraclitean themes of alteration and ongoing process, while Democritus imitated his ethical observations. Influenced by the teachings of the Heraclitean Cratylus, Plato saw the sensible world as exemplifying a Heraclitean flux. Plato and Aristotle both criticized Heraclitus for a radical theory that led to a denial of the Law of Non-Contradiction. The Stoics adopted Heraclitus's physical principles as the basis for their theories.

Barnes, Jonathan. The Presocratic Philosophers. London: Routledge & Kegan Paul, 1982 (1 vol. edn.). Ch. 4.

Uses modern arguments to defend the traditional view, going back to Plato and Aristotle, that Heraclitus' commitment to the flux doctrine and the identity of opposites results in an incoherent theory.

Graham, Daniel W. "Heraclitus' Criticism of Ionian Philosophy." Oxford Studies in Ancient Philosophy 15 (1997): 1-50.

Defends Heraclitus against the traditional view held by Barnes and others, and argues that his theory can be understood as a coherent criticism of earlier Ionian philosophy.

Hussey, Edward. "Epistemology and Meaning in Heraclitus." Language and Logos. Ed. M. Schofield and M. C. Nussbaum. Cambridge: Cambridge UP, 1982. 33-59.

Kahn, Charles H. The Art and Thought of Heraclitus. Cambridge: Cambridge UP, 1979.

An important reassessment of Heraclitus that recognizes the literary complexity of his language as a key to interpreting his message. Focuses on Heraclitus as a philosopher of the human condition.

Kirk, G. S. Heraclitus: The Cosmic Fragments. Cambridge: Cambridge UP, 1954.

Marcovich, Miroslav. Heraclitus: Greek Text with a Short Commentary. Merida, Venezuela: U. of the Andes, 1967.

A very thorough edition of Heraclitus, which effectively sorts out fragments from reports and reactions.

Mourelatos, Alexander P. D. "Heraclitus, Parmenides, and the Naive Metaphysics of Things." Exegesis and Argument. Ed. E. N. Lee et al. Assen: Van Gorcum, 1973. 16-48.

Examines Heraclitus' response to the pre-philosophical understanding of things.

Nussbaum, Martha C. "Psychê in Heraclitus." Phronesis 17 (1972): 1-16, 153-70.

Vlastos, Gregory. "On Heraclitus." American Journal of Philology 76 (1955): 337-68. Repr. in G. Vlastos, Studies in Greek Philosophy, vol. 1, Princeton: Princeton U. Pr., 1995.

Vigorous defense of the traditional interpretation of Heraclitus against Kirk and others.

Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure.

We do have details of Pythagoras's life from early biographies which use important original sources yet are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure. What we present below is an attempt to collect together the most reliable sources to reconstruct an account of Pythagoras's life. There is fairly good agreement on the main events of his life but most of the dates are disputed with different scholars giving dates which differ by 20 years. Some historians treat all this information as merely legends but, even if the reader treats it in this way, being such an early record it is of historical importance.

Pythagoras's father was Mnesarchus ([12] and [13]), while his mother was Pythais [8] and she was a native of Samos. Mnesarchus was a merchant who came from Tyre, and there is a story ([12] and [13]) that he brought corn to Samos at a time of famine and was granted citizenship of Samos as a mark of gratitude. As a child Pythagoras spent his early years in Samos but travelled widely with his father. There are accounts of Mnesarchus returning to Tyre with Pythagoras and that he was taught there by the Chaldaeans and the learned men of Syria. It seems that he also visited Italy with his father.

Little is known of Pythagoras's childhood. All accounts of his physical appearance are likely to be fictitious except the description of a striking birthmark which Pythagoras had on his thigh. It is probable that he had two brothers although some sources say that he had three. Certainly he was well educated, learning to play the lyre, learning poetry and to recite Homer. There were, among his teachers, three philosophers who were to influence Pythagoras while he was a young man. One of the most important was Pherekydes who many describe as the teacher of Pythagoras.

The other two philosophers who were to influence Pythagoras, and to introduce him to mathematical ideas, were Thales and his pupil Anaximander who both lived on Miletus. In [8] it is said that Pythagoras visited Thales in Miletus when he was between 18 and 20 years old. By this time Thales was an old man and, although he created a strong impression on Pythagoras, he probably did not teach him a great deal. However he did contribute to Pythagoras's interest in mathematics and astronomy, and advised him to travel to Egypt to learn more of these subjects. Thales's pupil, Anaximander, lectured on Miletus and Pythagoras attended these lectures. Anaximander certainly was interested in geometry and cosmology and many of his ideas would influence Pythagoras's own views.

In about 535 BC Pythagoras went to Egypt. This happened a few years after the tyrant Polycrates seized control of the city of Samos. There is some evidence to suggest that Pythagoras and Polycrates were friendly at first and it is claimed [5] that Pythagoras went to Egypt with a letter of introduction written by Polycrates. In fact Polycrates had an alliance with Egypt and there were therefore strong links between Samos and Egypt at this time. The accounts of Pythagoras's time in Egypt suggest that he visited many of the temples and took part in many discussions with the priests. According to Porphyry ([12] and [13]) Pythagoras was refused admission to all the temples except the one at Diospolis where he was accepted into the priesthood after completing the rites necessary for admission.

It is not difficult to relate many of Pythagoras's beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt. For example the secrecy of the Egyptian priests, their refusal to eat beans, their refusal to wear even cloths made from animal skins, and their striving for purity were all customs that Pythagoras would later adopt. Porphyry in [12] and [13] says that Pythagoras learnt geometry from the Egyptians but it is likely that he was already acquainted with geometry, certainly after teachings from Thales and Anaximander.

In 525 BC Cambyses II, the king of Persia, invaded Egypt. Polycrates abandoned his alliance with Egypt and sent 40 ships to join the Persian fleet against the Egyptians. After Cambyses had won the Battle of Pelusium in the Nile Delta and had captured Heliopolis and Memphis, Egyptian resistance collapsed. Pythagoras was taken prisoner and taken to Babylon. Iamblichus writes that Pythagoras (see [8]):-

... was transported by the followers of Cambyses as a prisoner of war. Whilst he was there he gladly associated with the Magoi ... and was instructed in their sacred rites and learnt about a very mystical worship of the gods. He also reached the acme of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians...

In about 520 BC Pythagoras left Babylon and returned to Samos. Polycrates had been killed in about 522 BC and Cambyses died in the summer of 522 BC, either by committing suicide or as the result of an accident. The deaths of these rulers may have been a factor in Pythagoras's return to Samos but it is nowhere explained how Pythagoras obtained his freedom. Darius of Persia had taken control of Samos after Polycrates' death and he would have controlled the island on Pythagoras's return. This conflicts with the accounts of Porphyry and Diogenes Laertius who state that Polycrates was still in control of Samos when Pythagoras returned there.

Pythagoras made a journey to Crete shortly after his return to Samos to study the system of laws there. Back in Samos he founded a school which was called the semicircle. Iamblichus [8] writes in the third century AD that:-

... he formed a school in the city [of Samos], the 'semicircle' of Pythagoras, which is known by that name even today, in which the Samians hold political meetings. They do this because they think one should discuss questions about goodness, justice and expediency in this place which was founded by the man who made all these subjects his business. Outside the city he made a cave the private site of his own philosophical teaching, spending most of the night and daytime there and doing research into the uses of mathematics...

Pythagoras left Samos and went to southern Italy in about 518 BC (some say much earlier). Iamblichus [8] gives some reasons for him leaving. First he comments on the Samian response to his teaching methods:-

... he tried to use his symbolic method of teaching which was similar in all respects to the lessons he had learnt in Egypt. The Samians were not very keen on this method and treated him in a rude and improper manner.

This was, according to Iamblichus, used in part as an excuse for Pythagoras to leave Samos:-

... Pythagoras was dragged into all sorts of diplomatic missions by his fellow citizens and forced to participate in public affairs. ... He knew that all the philosophers before him had ended their days on foreign soil so he decided to escape all political responsibility, alleging as his excuse, according to some sources, the contempt the Samians had for his teaching method.

Pythagoras founded a philosophical and religious school in Croton (now Crotone, on the east of the heel of southern Italy) that had many followers. Pythagoras was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. The beliefs that Pythagoras held were [2]:-

(1) that at its deepest level, reality is mathematical in nature,
(2) that philosophy can be used for spiritual purification,
(3) that the soul can rise to union with the divine,
(4) that certain symbols have a mystical significance, and
(5) that all brothers of the order should observe strict loyalty and secrecy.

Both men and women were permitted to become members of the Society, in fact several later women Pythagoreans became famous philosophers. The outer circle of the Society were known as the akousmatics and they lived in their own houses, only coming to the Society during the day. They were allowed their own possessions and were not required to be vegetarians.

Of Pythagoras's actual work nothing is known. His school practised secrecy and communalism making it hard to distinguish between the work of Pythagoras and that of his followers. Certainly his school made outstanding contributions to mathematics, and it is possible to be fairly certain about some of Pythagoras's mathematical contributions. First we should be clear in what sense Pythagoras and the mathematikoi were studying mathematics. They were not acting as a mathematics research group does in a modern university or other institution. There were no 'open problems' for them to solve, and they were not in any sense interested in trying to formulate or solve mathematical problems.

Rather Pythagoras was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of a proof. As Brumbaugh writes in [3]:-

It is hard for us today, familiar as we are with pure mathematical abstraction and with the mental act of generalisation, to appreciate the originality of this Pythagorean contribution.

In fact today we have become so mathematically sophisticated that we fail even to recognise 2 as an abstract quantity. There is a remarkable step from 2 ships + 2 ships = 4 ships, to the abstract result 2 + 2 = 4, which applies not only to ships but to pens, people, houses etc. There is another step to see that the abstract notion of 2 is itself a thing, in some sense every bit as real as a ship or a house.

Pythagoras believed that all relations could be reduced to number relations. As Aristotle wrote:-

The Pythagorean ... having been brought up in the study of mathematics, thought that things are numbers ... and that the whole cosmos is a scale and a number.

This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy. Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. In fact Pythagoras made remarkable contributions to the mathematical theory of music. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill.

Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers etc. However to Pythagoras numbers had personalities which we hardly recognise as mathematics today [3]:-

Each number had its own personality - masculine or feminine, perfect or incomplete, beautiful or ugly. This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Ten was the very best number: it contained in itself the first four integers - one, two, three, and four [1 + 2 + 3 + 4 = 10] - and these written in dot notation formed a perfect triangle.

Of course today we particularly remember Pythagoras for his famous geometry theorem. Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians 1000 years earlier he may have been the first to prove it. Proclus, the last major Greek philosopher, who lived around 450 AD wrote (see [7]):-

After [Thales, etc.] Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrational and the construction of the cosmic figures.

I emulate the Pythagoreans who even had a conventional phrase to express what I mean "a figure and a platform, not a figure and a sixpence", by which they implied that the geometry which is deserving of study is that which, at each new theorem, sets up a platform to ascend by, and lifts the soul on high instead of allowing it to go down among the sensible objects and so become subservient to the common needs of this mortal life.

Heath [7] gives a list of theorems attributed to Pythagoras, or rather more generally to the Pythagoreans.

(i) The sum of the angles of a triangle is equal to two right angles. Also the Pythagoreans knew the generalisation which states that a polygon with n sides has sum of interior angles 2n - 4 right angles and sum of exterior angles equal to four right angles.

(ii) The theorem of Pythagoras - for a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side. To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square.

(iii) Constructing figures of a given area and geometrical algebra. For example they solved equations such as a (a - x) = x² by geometrical means.

(iv) The discovery of irrationals. This is certainly attributed to the Pythagoreans but it does seem unlikely to have been due to Pythagoras himself. This went against Pythagoras's philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers. However, because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number.

(v) The five regular solids. It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he would have known how to construct the other two.

(vi) In astronomy Pythagoras taught that the Earth was a sphere at the centre of the Universe. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star.

Primarily, however, Pythagoras was a philosopher. In addition to his beliefs about numbers, geometry and astronomy described above, he held [2]:-

... the following philosophical and ethical teachings: ... the dependence of the dynamics of world structure on the interaction of contraries, or pairs of opposites; the viewing of the soul as a self-moving number experiencing a form of metempsychosis, or successive reincarnation in different species until its eventual purification (particularly through the intellectual life of the ethically rigorous Pythagoreans); and the understanding ...that all existing objects were fundamentally composed of form and not of material substance. Further Pythagorean doctrine ... identified the brain as the locus of the soul; and prescribed certain secret cultic practices.

In their ethical practices, the Pythagorean were famous for their mutual friendship, unselfishness, and honesty.

Pythagoras's Society at Croton was not unaffected by political events despite his desire to stay out of politics. Pythagoras went to Delos in 513 BC to nurse his old teacher Pherekydes who was dying. He remained there for a few months until the death of his friend and teacher and then returned to Croton. In 510 BC Croton attacked and defeated its neighbour Sybaris and there is certainly some suggestions that Pythagoras became involved in the dispute. Then in around 508 BC the Pythagorean Society at Croton was attacked by Cylon, a noble from Croton itself. Pythagoras escaped to Metapontium and the most authors say he died there, some claiming that he committed suicide because of the attack on his Society. Iamblichus in [8] quotes one version of events:-

Cylon, a Crotoniate and leading citizen by birth, fame and riches, but otherwise a difficult, violent, disturbing and tyrannically disposed man, eagerly desired to participate in the Pythagorean way of life. He approached Pythagoras, then an old man, but was rejected because of the character defects just described. When this happened Cylon and his friends vowed to make a strong attack on Pythagoras and his followers. Thus a powerfully aggressive zeal activated Cylon and his followers to persecute the Pythagoreans to the very last man. Because of this Pythagoras left for Metapontium and there is said to have ended his days.

This seems accepted by most but Iamblichus himself does not accept this version and argues that the attack by Cylon was a minor affair and that Pythagoras returned to Croton. Certainly the Pythagorean Society thrived for many years after this and spread from Croton to many other Italian cities. Gorman [6] argues that this is a strong reason to believe that Pythagoras returned to Croton and quotes other evidence such as the widely reported age of Pythagoras as around 100 at the time of his death and the fact that many sources say that Pythagoras taught Empedokles to claim that he must have lived well after 480 BC.

The evidence is unclear as to when and where the death of Pythagoras occurred. Certainly the Pythagorean Society expanded rapidly after 500 BC, became political in nature and also spilt into a number of factions. In 460 BC the Society [2]:-

... was violently suppressed. Its meeting houses were everywhere sacked and burned; mention is made in particular of "the house of Milo" in Croton, where 50 or 60 Pythagoreans were surprised and slain. Those who survived took refuge at Thebes and other places.

He mistrusted senses as much as Heraclitus did due to his aristocratic cradle, but was much more harmful than Heraclitus with regard to his speculative philosophical conclusions. He held that the senses were not to be relied upon but went a step further and came to the arbitrary conclusion that MOVEMENT did not exist, that it was an optical illusion, that change did not exist, that everything was still and quiet. In order to emphasize his ideas, he created the dictum: What is, is, what is not, isn’t. He thus killed two birds with a stone: no change, and no empty spaces, no processes of rarification or condensation. The world is a solid sphere, uncreated, indestructible. Motionless and immutable. Like God with whom Parmenides identified the world, to be sure, it is the same yesterday, today and always.

Parmenides was a Greek philosopher and poet, born of an illustrious family about BCE. 510, at Elea in Lower Italy, and is is the chief representative of the Eleatic philosophy. He was held in high esteem by his fellow-citizens for his excellent legislation, to which they ascribed the prosperity and wealth of the town. He was also admired for his exemplary life. A "Parmenidean life" was proverbial among the Greeks. He is commonly represented as a disciple of Xenophanes. Parmenides wrote after Heraclitus, and in conscious opposition to him, given the evident allusion to Hericlitus: "for whom it is and is not, the same and not the same, and all things travel in opposite directions" (fr. 6, 8). Little more is known of his biography than that he stopped at Athens on a journey in his sixty-fifth year, and there became acquainted with the youthful Socrates. That must have been in the middle of the fifth century BCE., or shortly after it.

Parmenides broke with the older Ionic prose tradition by writing in hexameter verse. His didactic poem, called On Nature, survives in fragments, although the Proem (or introductory discourse) of the work has been preserved. Parmenides was a young man when he wrote it, for the goddess who reveals the truth to him addresses him as 'youth'. The work is considered inartistic. Its Hesiodic style was appropriate for the cosmogony he describes in the second part, but is unsuited to the arid dialectic of the first. Parmenides was no born poet, and we much ask what led him to take this new departure. The example of Xenophanes' poetic writings is not a complete explanation; for the poetry of Parmenides is as unlike that of Xenophanes as it well can be, and his style is more like Hesiod and the Orphics. In the Proem Parmenides describes his ascent to the home of the goddess who is supposed to speak the remainder of the verses; this is a reflexion of the conventional ascents into heaven which were almost as common as descents into hell in the apocalyptic literature of those days.

The Proem opens with Parmenides representing himself as borne on a chariot and attended by the Sunmaidens who have quitted the Halls of Night to guide him on his journey. They pass along the highway till they come to the Gate of Night and Day, which is locked and barred. The key is in the keeping of Dike (Right), the Avenger, who is persuaded to unlock it by the Sunmaidens. They pass in through the gate and are now, of course, in the realms of Day. The goal of the journey is the palace of a goddess who welcomes Parmenides and instructs him in the two ways, that of Truth and the deceptive way of Belief, in which is no truth at all. All this is described without inspiration and in a purely conventional manner, so it must be interpreted by the canons of the apocalyptic style. It is clearly meant to indicate that Parmenides had been converted, that he had passed from error (night) to truth (day), and the Two Ways must represent his former error and the truth which is now revealed to him.

There is reason to believe that the Way of Belief is an account of Pythagorean cosmology. In any case, it is surely impossible to regard it as anything else than a description of some error. The goddess says so in words that cannot be explained away. Further, this erroneous belief is not the ordinary man's view of the world, but an elaborate system, which seems to be a natural development the Ionian cosmology on certain lines, and there is no other system but the Pythagorean that fulfils this requirement. To this it has been objected that Parmenides would not have taken the trouble to expound in detail a system he had altogether rejected, but that is to mistake the character of the apocalyptic convention. It is not Parmenides, but the goddess, that expounds the system, and it is for this reason that the beliefs described are said to be those of 'mortals'. Now a description of the ascent of the soul would be quite incomplete without a picture of the region from which it had escaped. The goddess must reveal the two ways at the parting of which Parmenides stands, and bid him choose the better. The rise of mathematics in the Pythagorean school had revealed for the first time the power of thought. To the mathematician of all men it is the same thing that can be thought and that can be, and this is the principle from which Parmenides starts. It is impossible to think what is not, and it is impossible for what cannot be thought to be. The great question, Is it or is it not? is therefore equivalent to the question, Can it be thought or not?

In any case, the work thus has two divisions. The first discusses the truth, and the second the world of illusion -- that is, the world of the senses and the erroneous opinions of mankind founded upon them. In his opinion truth lies in the perception that existence is, and error in the idea that non-existence also can be. Nothing can have real existence but what is conceivable; therefore to be imagined and to be able to exist are the same thing, and there is no development. The essence of what is conceivable is incapable of development, imperishable, immutable, unbounded, and indivisible. What is various and mutable, all development, is a delusive phantom. Perception is thought directed to the pure essence of being; the phenomenal world is a delusion, and the opinions formed concerning it can only be improbable.

Parmenides goes on to consider in the light of this principle the consequences of saying that anything is. In the first place, it cannot have come into being. If it had, it must have arisen from nothing or from something. It cannot have arisen from nothing; for there is no nothing. It cannot have arisen from something; for here is nothing else than what is. Nor can anything else besides itself come into being; for there can be no empty space in which it could do so. Is it or is it not? If it is, then it is now, all at once. In this way Parmenides refutes all accounts of the origin of the world. Ex nihilo nihil fit.

Further, if it is, it simply is, and it cannot be more or less. There is, therefore, as much of it in one place as in another. (That makes rarefaction and condensation impossible.) it is continuous and indivisible; for there is nothing but itself which could prevent its parts being in contact with on another. It is therefore full, a continuous indivisible plenum. (That is directed against the Pythagorean theory of a discontinuous reality.) Further, it is immovable. If it moved, it must move into empty space, and empty space is nothing, and there is no nothing. Also it is finite and spherical; for it cannot be in one direction any more than in another, and the sphere is the only figure of which this can be said. What is is, therefore a finite, spherical, motionless, continuous plenum, and there is nothing beyond it. Coming into being and ceasing to be are mere 'names', and so is motion, and still more color and the like. They are not even thoughts; for a thought must be a thought of something that is, and none of these can be.

Such is the conclusion to which the view of the real as a single body inevitably leads, and there is no escape from it. The 'matter' of our physical text-books is just the real of Parmenides; and, unless we can find room for something else than matter, we are shut up into his account of reality. No subsequent system could afford to ignore this, but of course it was impossible to acquiesce permanently in a doctrine like that of Parmenides. It deprives the world we know of all claim to existence, and reduces it to something which is hardly even an illusion. If we are to give an intelligible account of the world, we must certainly introduce motion again somehow. That can never be taken for granted any more, as it was by the early cosmologists; we must attempt to explain it if we are to escape from the conclusions of Parmenides.

Very little is known of the life of Zeno of Elea. We certainly know that he was a philosopher, and he is said to have been the son of Teleutagoras. The main source of our knowledge of Zeno comes from the dialogue Parmenides written by Plato.

Zeno was a pupil and friend of the philosopher Parmenides and studied with him in Elea. The Eleatic School, one of the leading pre-Socratic schools of Greek philosophy, had been founded by Parmenides in Elea in southern Italy. His philosophy of monism claimed that the many things which appear to exist are merely a single eternal reality which he called Being. His principle was that "all is one" and that change or non-Being are impossible. Certainly Zeno was greatly influenced by the arguments of Parmenides and Plato tells us that the two philosophers visited Athens together in around 450 BC.

Despite Plato's description of the visit of Zeno and Parmenides to Athens, it is far from universally accepted that the visit did indeed take place. However, Plato tell us that Socrates, who was then young, met Zeno and Parmenides on their visit to Athens and discussed philosophy with them. Given the best estimates of the dates of birth of these three philosophers, Socrates would be about 20, Zeno about 40, and Parmenides about 65 years of age at the time, so Plato's claim is certainly possible.

Zeno had already written a work on philosophy before his visit to Athens and Plato reports that Zeno's book meant that he had achieved a certain fame in Athens before his visit there. Unfortunately no work by Zeno has survived, but there is very little evidence to suggest that he wrote more than one book. The book Zeno wrote before his visit to Athens was his famous work which, according to Proclus, contained forty paradoxes concerning the continuum. Four of the paradoxes, which we shall discuss in detail below, were to have a profound influence on the development of mathematics.

Diogenes Laertius [10] gives further details of Zeno's life which are generally thought to be unreliable. Zeno returned to Elea after the visit to Athens and Diogenes Laertius claims that he met his death in a heroic attempt to remove a tyrant from the city of Elea. The stories of his heroic deeds and torture at the hands of the tyrant may well be pure inventions. Diogenes Laertius also writes about Zeno's cosmology and again there is no supporting evidence regarding this, but we shall give some indication below of the details.

... a youthful effort, and it was stolen by someone, so that the author had no opportunity of considering whether to publish it or not. Its object was to defend the system of Parmenides by attacking the common conceptions of things.

... Zeno elaborated forty different paradoxes following from the assumption of plurality and motion, all of them apparently based on the difficulties deriving from an analysis of the continuum.

In his arguments against the idea that the world contains more than one thing, Zeno derived his paradoxes from the assumption that if a magnitude can be divided then it can be divided infinitely often. Zeno also assumes that a thing which has no magnitude cannot exist. Simplicius, the last head of Plato's Academy in Athens, preserved many fragments of earlier authors including Parmenides and Zeno. Writing in the first half of the sixth century he explained Zeno's argument why something without magnitude could not exist [1]:-

For if it is added to something else, it will not make it bigger, and if it is subtracted, it will not make it smaller. But if it does not make a thing bigger when added to it nor smaller when subtracted from it, then it appears obvious that what was added or subtracted was nothing.

Although Zeno's argument is not totally convincing at least, as Makin writes in [25]:-

Zeno's challenge to simple pluralism is successful, in that he forces anti-Parmenideans to go beyond common sense.

The paradoxes that Zeno gave regarding motion are more perplexing. Aristotle, in his work Physics, gives four of Zeno's arguments, The Dichotomy, The Achilles, The Arrow, and The Stadium. For the dichotomy, Aristotle describes Zeno's argument (in Heath's translation [8]):-

There is no motion because that which is moved must arrive at the middle of its course before it arrives at the end.

In order the traverse a line segment it is necessary to reach its midpoint. To do this one must reach the ¹/₄ point, to do this one must reach the ¹/₈ point and so on ad infinitum. Hence motion can never begin. The argument here is not answered by the well known infinite sum

On the one hand Zeno can argue that the sum ¹/₂ + ¹/₄ + ¹/₈ + ... never actually reaches 1, but more perplexing to the human mind is the attempts to sum ¹/₂ + ¹/₄ + ¹/₈ + ... backwards. Before traversing a unit distance we must get to the middle, but before getting to the middle we must get ¹/₄ of the way, but before we get ¹/₄ of the way we must reach ¹/₈ of the way etc. This argument makes us realise that we can never get started since we are trying to build up this infinite sum from the "wrong" end. Indeed this is a clever argument which still puzzles the human mind today.

Zeno bases both the dichotomy paradox and the attack on simple pluralism on the fact that once a thing is divisible, then it is infinitely divisible. One could counter his paradoxes by postulating an atomic theory in which matter was composed of many small indivisible elements. However other paradoxes given by Zeno cause problems precisely because in these cases he considers that seemingly continuous magnitudes are made up of indivisible elements. Such a paradox is 'The Arrow' and again we give Aristotle's description of Zeno's argument (in Heath's translation [8]):-

If, says Zeno, everything is either at rest or moving when it occupies a space equal to itself, while the object moved is in the instant, the moving arrow is unmoved.

The argument rests on the fact that if in an indivisible instant of time the arrow moved, then indeed this instant of time would be divisible (for example in a smaller 'instant' of time the arrow would have moved half the distance). Aristotle argues against the paradox by claiming:-

... for time is not composed of indivisible 'nows', no more than is any other magnitude.

However, this is considered by some to be irrelevant to Zeno's argument. Moreover to deny that 'now' exists as an instant which divides the past from the future seems also to go against intuition. Of course if the instant 'now' does not exist then the arrow never occupies any particular position and this does not seem right either. Again Zeno has presented a deep problem which, despite centuries of efforts to resolve it, still seems to lack a truly satisfactory solution. As Frankel writes in [20]:-

The human mind, when trying to give itself an accurate account of motion, finds itself confronted with two aspects of the phenomenon. Both are inevitable but at the same time they are mutually exclusive. Either we look at the continuous flow of motion; then it will be impossible for us to think of the object in any particular position. Or we think of the object as occupying any of the positions through which its course is leading it; and while fixing our thought on that particular position we cannot help fixing the object itself and putting it at rest for one short instant.

Vlastos (see [32]) points out that if we use the standard mathematical formula for velocity we have v = s/t, where s is the distance travelled and t is the time taken. If we look at the velocity at an instant we obtain v = ⁰/₀, which is meaningless. So it is fair to say that Zeno here is pointing out a mathematical difficulty which would not be tackled properly until limits and the differential calculus were studied and put on a proper footing.

As can be seen from the above discussion, Zeno's paradoxes are important in the development of the notion of infinitesimals. In fact some authors claim that Zeno directed his paradoxes against those who were introducing infinitesimals. Anaxagoras and the followers of Pythagoras, with their development of incommensurables, are also thought by some to be the targets of Zeno's arguments (see for example [10]). Certainly it appears unlikely that the reason given by Plato, namely to defend Parmenides' philosophical position, is the whole explanation of why Zeno wrote his famous work on paradoxes.

The most famous of Zeno's arguments is undoubtedly the Achilles. Heath's translation from Aristotle's Physics is:-

... the slower when running will never be overtaken by the quicker; for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must necessarily always be some distance ahead.

Most authors, starting with Aristotle, see this paradox to be essentially the same as the Dichotomy. For example Makin [25] writes:-

... as long as the Dichotomy can be resolved, the Achilles can be resolved. The resolutions will be parallel.

As with most statements about Zeno's paradoxes, there is not complete agreement about any particular position. For example Toth [29] disputes the similarity of the two paradoxes, claiming that Aristotle's remarks leave much to be desired and suggests that the two arguments have entirely different structures.

Both Plato and Aristotle did not fully appreciate the significance of Zeno's arguments. As Heath says [8]:-

Russell certainly did not underrate Zeno's significance when he wrote in [13]:-

In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgement is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance ....

Here Russell is thinking of the work of Cantor, Frege and himself on the infinite and particularly of Weierstrass on the calculus. In [2] the relation of the paradoxes to mathematics is also discussed, and the author comes to a conclusion similar to Frankel in the above quote:-

Although they have often been dismissed as logical nonsense, many attempts have also been made to dispose of them by means of mathematical theorems, such as the theory of convergent series or the theory of sets. In the end, however, the difficulties inherent in his arguments have always come back with a vengeance, for the human mind is so constructed that it can look at a continuum in two ways that are not quite reconcilable.

It is difficult to tell precisely what effect the paradoxes of Zeno had on the development of Greek mathematics. B L van der Waerden (see [31]) argues that the mathematical theories which were developed in the second half of the fifth century BC suggest that Zeno's work had little influence. Heath however seems to detect a greater influence [8]:-

Mathematicians, however, ... realising that Zeno's arguments were fatal to infinitesimals, saw that they could only avoid the difficulties connected with them by once and for all banishing the idea of the infinite, even the potentially infinite, altogether from their science; thenceforth, therefore, they made no use of magnitudes increasing or decreasing ad infinitum, but contented themselves with finite magnitudes that can be made as great or as small as we please.

We commented above that Diogenes Laertius in [10] describes a cosmology that he believes is due to Zeno. According to his description, Zeno proposed a universe consisting of several worlds, composed of "warm" and "cold, "dry" and "wet" but no void or empty space. Because this appears to have nothing in common with his paradoxes, it is usual to take the line that Diogenes Laertius is in error. However, there is some evidence that this type of belief was around in the fifth century BC, particularly associated with medical theory, and it could easily have been Zeno's version of a belief held by the Eleatic School.

Alcmaeon

Alcmaeon of Croton was an early Greek medical writer and philosopher-scientist. His exact date, his relationship to other early Greek philosopher-scientists, and whether he was primarily a medical writer/physician or a typical Presocratic cosmologist, are all matters of controversy. He is likely to have written his book sometime between 500 and 450 BC. The surviving fragments and testimonia focus primarily on issues of psychology and epistemology and reveal Alcmaeon to be a thinker of considerable originality. He was the first to identify the brain as the seat of understanding and to distinguish understanding from perception. Alcmaeon thought that the sensory organs were connected to the brain by channels (poroi) and may have discovered the poroi connecting the eyes to the brain (i.e. the optic nerve) by excising the eyeball of an animal, although it is doubtful that he used dissection as a standard method. He was the first to develop an argument for the immortality of the soul. He used a political metaphor to define health and disease: The equality (isonomia) of the opposing powers which make up the body (e.g., the wet, the dry, the hot, the cold, the sweet, the bitter etc.) preserve health, whereas the monarchy of any one of them produces disease. Alcmaeon discussed a wide range of topics in physiology including sleep, death and the development of the embryo. It is unclear whether he also presented a cosmology in terms of opposing powers, but we do have some testimonia concerning his views on astronomy. Alcmaeon had considerable impact on his successors in the Greek philosophical tradition. Aristotle wrote a treatise responding to him, Plato adopted his argument for the immortality of the soul, and both Plato and Philolaus accepted his view that the brain is the seat of intelligence.

Life and Works

1.1 Medical Writer or Philosopher?

Alcmaeon, son of Peirithous (otherwise unknown), lived in the Greek city of Croton on the instep of the boot of Italy. Diogenes Laertius, in his brief life of Alcmaeon (VIII. 83), asserts that he wrote mostly on medical matters. There is, however, little direct evidence for his work as a practicing physician. Later writers in the medical tradition, such as Galen (DK A2), treat him as a philosopher-scientist rather than as a physician, so that some scholars (Mansfeld 1975) have concluded that he was not a doctor at all but rather a typical Presocratic physiologos (writer on nature). The majority of scholars, however, because of Diogenes' remark and because of the focus on the functioning of the human body in the testimonia and fragments, refer to Alcmaeon as a physician-philosopher. The historian Herodotus tells us that, in the second half of the sixth century, the physicians of Croton were the best in the Greek world (III. 131) and recounts in some detail the activities of the most prominent Crotoniate physician of the time, Democedes (III. 125-138). Thus, whether a practicing physician or not, Alcmaeon undoubtedly owes some of his interest in human physiology and psychology to the medical tradition in Croton. At this point in the history of Greek thought, it is difficult to draw clear lines between the work of a medical writer/physician and a philosopher/scientist. Most Presocratic cosmologies devoted some attention to questions of human physiology and medicine, and conversely the early treatises in the Hippocratic corpus often paid some attention to cosmology (see Aristotle, Resp. 480b23 ff.).

1.2 Was Alcmaeon a Pythagorean?

Croton is also famous as the center of Pythagoras' activity from ca. 530, when he left Samos, until his death ca. 490. Alcmaeon addressed his book to three men who may have been Pythagoreans:

Alcmaeon of Croton, son of Peirithous, said the following to Brotinus, Leon and Bathyllus... (B 1)

We know nothing of Leon and Bathyllus, except that Iamblichus, in On the Pythagorean Way of Life (=VP), lists a Pythagorean named Leon from Metapontum and a Pythagorean Bathylaus from Poseidonia (Paestum), both Greek cities of southern Italy (VP 267). Bro(n)tinus is identified as a Pythagorean from Croton in some places (D.L. VIII. 42; Iamb. VP 132) and from Metapontum in others (VP 194, 267). He is either the father or the husband of Theano, who is in turn either the wife or student of Pythagoras. Does this "dedication" of his book to Pythagoreans indicate that Alcmaeon himself was a Pythagorean? Even if this is a dedication, it does not follow that Alcmaeon agreed with the views of his addressees. Comparison with Empedocles' address to Pausanias suggests, moreover, that what we have is not a dedication but an exhortation or an attempt to instruct (Vlastos 1953, 344, n. 25). Alcmaeon might be quite independent of these Pythagoreans and trying to persuade them of his distinct point of view.

Diogenes Laertius, in his Lives of the Philosophers (3^rd century AD), includes Alcmaeon among the Pythagoreans and says that he studied with Pythagoras (VIII. 83). Later authors such as Iamblichus (VP 104, 267), Philoponus (De An. p. 88) and the scholiast on Plato (Alc. 121e) also call Alcmaeon a Pythagorean. A majority of scholars up to the middle of the twentieth century followed this tradition. On the other hand, no one earlier than Diogenes calls Alcmaeon a Pythagorean. Aristotle wrote two books on the Pythagoreans but wrote a separate book on Alcmaeon. Aristotle and Theophrastus refer to him a number of times but never identify him as a Pythagorean, and this is the practice of the doxographical tradition (see A4, 6, 8-10, 13-14, 17-18, in DK 24). Simplicius (6^th AD) reports that some have handed down the view that Alcmaeon is a Pythagorean but notes that Aristotle denies it (De An. 32.3). Most telling is Aristotle's discussion of Alcmaeon in Metaphysics book I (986a22 ff.). He notes a similarity between Alcmaeon and a group of Pythagoreans in positing opposites as the principles of things but expresses uncertainty as to who influenced whom. Earlier scholars took this comparison of Alcmaeon to the Pythagoreans as confirmation that he was a Pythagorean. Most scholars of the last fifty years, however, have come to recognize that Aristotle's treatment of Alcmaeon here suggests the exact opposite; it only makes sense to compare him with the Pythagoreans and wonder who influenced whom, if he is not a Pythagorean (e.g., Lloyd 1991, 167). Certainly most of the opposites which are mentioned as crucial to Alcmaeon do not appear in the Pythagorean table of opposites, and there is no trace of the crucial Pythagorean opposition between limit and unlimited in Alcmaeon. The overwhelming majority of scholars since 1950 have accordingly regarded Alcmaeon as a figure independent of the Pythagoreans (e.g., Guthrie 1962 and Lloyd 1991, 167; Zhmud 1997, 70-71, is one of the few exceptions), although, as a fellow citizen of Croton, he will have been familiar with their thought.

1.3 Date

No issue concerning Alcmaeon has been more controversial than his date. Some have sought to date him on the basis of his address to Brotinus. Brotinus' dates are too uncertain to be of much help, however. If he is Theano's father and Theano was Pythagoras' wife, he could be a contemporary of Pythagoras (570-490) or even older. If he is Theano's husband and she was a student of Pythagoras in his old age and thus twenty in 490, Brotinus could have been born as late as 520. This suggests that Brotinus could have been the addressee of the book any time between 550 and 450 BC. The center of controversy, however, has been a sentence in the passage of Aristotle's Metaphysics discussed above:

Alcmaeon of Croton also seems to have thought along similar lines, and either he took this theory over from them [i.e. the Pythagoreans] or they from him. For in age Alcmaeon was in the old age of Pythagoras, and his views were similar to theirs (986a27-31).

The sentence in bold above is missing in one of the major manuscripts and Alexander makes no mention of it in his commentary on the Metaphysics. It does appear in the other two major manuscripts and in Asclepius' commentary. A number of scholars have regarded it as a remark written in the margin by a later commentator, which has crept into the text (e.g., Ross 1924, 152; Burkert 1972, 29, n.60). It is a surprising remark for Aristotle to make, since he only refers to Pythagoras once elsewhere in all his extant writings and throughout this passage of the Metaphysics refers to the Pythagoreans or Italians in the plural. An almost equal number of scholars regard the remark as genuine (e.g., Wachtler 1896; Guthrie 1962, 341-3). Even if we accept the remark as genuine, the assertion that Alcmaeon "was" (egeneto) in the old age of Pythagoras is ambiguous. Does it mean that Alcmaeon was born in the old age of Pythagoras, or that he lived in the old age of Pythagoras? Diels emended the sentence to say that Alcmaeon was "young" in the old age of Pythagoras and a similar remark can be found in Iamblichus (VP 104). Although Diels accepted the text as Aristotelian, others have seen the parallel with Iamblichus as evidence that it is a remark by a later commentator and have pointed out that the report in Iamblichus involves several chronological impossibilities (e.g., that Philolaus was young in the old age of Pythagoras). Whatever the provenance of the remark, scholars have been influenced by it, because there is little else to go on. One group of scholars dates the publication of Alcmaeon's book to around 500 (Burkert 1972, 292; Kirk, Raven, Schofield 1983, 339 [early 5^th]) so that he would have been born around 540. Another group has him born around 510 so that his book would have been published in 470 or later (Guthrie 1962, 358 [480-440 BC]; Lloyd 1991, 168 [490-430 BC]. In either case Alcmaeon probably wrote before Empedocles, Anaxagoras and Philolaus. He is either the contemporary or the predecessor of Parmenides. Attempts to date him on the basis of internal evidence alone, i.e. comparison of his doctrines with those of other thinkers, have led to the widest divergence of dates. Edelstein says that he may have lived in the late fifth century (1942, 372), while Lebedev makes him active in the late 6^th (1993).

1.4 Alcmaeon's Book and the Evidence for Its Contents

The ancient tradition assigns one book to Alcmaeon, which came to bear the traditional title of Presocratic treatises, On Nature (A2), although this title probably does not go back to Alcmaeon himself. Favorinus' report that Alcmaeon was the first to write such a treatise (A1) is almost certainly wrong, since Anaximander wrote before Alcmaeon. Theophrastus' detailed report of Alcmaeon's account of the senses (A5) and the fact that Aristotle wrote a treatise in response to Alcmaeon (D.L. V. 25) suggest that the book was available in the fourth century BC. It is unclear whether Alcmaeon wrote in the Doric dialect of Croton or in the Ionic Greek of the first Presocratics (Burkert, 1972, 222, n. 21). The report that an Alcimon of Croton was the first to write animal fables might be a reference to a poet of a similar name. Fragment 5 in DK ("It is easier to be on one's guard against an enemy than a friend.") sounds very much like the moral of such a fable (Gomperz 1953, 64-5). Diels and Kranz (=DK) identify five other fragments of Alcmaeon (Frs. 1, 1a, 2, 3, 4) and arrange the testimonia under 18 headings. Fragments 1a, 3 and 4, however, are really testimonia which use language of a later date, although some of Alcmaeon's terminology is embedded in them. The three lines of Fragment 1, which probably began the book, and the half line in Fragment 2 are the only continuous texts of Alcmaeon. Another brief fragment/testimonium should be added to the material in DK: "the earth is the mother of plants and the sun their father" (Nicolaus Damascenus, De plantis I 2.44; see Kirk 1956 and Lebedev 1993). There is also the possibility that Fr. 125 of the Spartan poet Alcman ("Experience is the beginning of learning.") should, in fact, be assigned to Alcmaeon (Lanza 1965; Barnes 1982, 610).

2. Epistemology and Psychology

2.1 The Limits of Knowledge

Concerning things that are not perceptible [and concerning mortal things] the gods have clarity, but insofar as it is possible for human beings to judge ...(B1)

Such skepticism about human knowledge is characteristic of one strand of early Greek thought. Both Alcmaeon's predecessors (e.g., Xenophanes B34) and his successors (e.g., Philolaus B6) made similar contrasts between divine and human knowledge, but in Alcmaeon's case, as in these other cases, we do not have enough evidence to be sure what he intended. Most of the subjects that Alcmaeon went on to discuss in his book could not be settled by a direct appeal to sense perception (e.g., the functioning of the senses, the balance of opposites in the healthy body, the immortality of the soul). In this sense he was dealing largely with what is "not perceptible" (aphanes). Alcmaeon is decidedly not an extreme skeptic, however, in that he is willing to assign clear understanding about such things to the gods and by implication admits that even humans have clear understanding of what is directly perceptible. Moreover, while humans cannot attain clarity about what cannot be perceived, Alcmaeon thinks that they can make reasonable judgments from the signs that are presented to them by sensation (tekmairesthai). He thus takes the stance of the scientist who draws inferences from what can be perceived, and he implicitly rejects the claims of those who base their account of the world on the certainty of a divine revelation (e.g., Pythagoras, Parmenides B1).

2.2 Understanding and Empiricism

According to Theophrastus, Alcmaeon was the first Greek thinker to distinguish between sense perception and understanding and to use this distinction to separate animals, which only have sense perception, from humans, who have both sense perception and understanding (B1a, A5). Alcmaeon is also the first to argue that the brain is the central organ of sensation and thought (A5, A8, A10). There is no explicit evidence, however, as to what Alcmaeon meant by understanding. The word translated as understanding here is suniêmi, which in its earliest uses means "to bring together," so that it is possible that Alcmaeon simply meant that humans are able to bring the information provided by the senses together in a way that animals cannot (Solmsen 1961, 151). Animals have brains too, however, and thus might appear to be able to carry out the simple correlation of the evidence from the various senses, whereas the human ability to make inferences and judgments (B1) appears to be a more plausible candidate for the distinctive activity of human intelligence. It is possible that we should use a passage in Plato's Phaedo (96a-b = A11) to explicate further Alcmaeon's epistemology. The passage is part of Socrates' report of his early infatuation with natural science and with questions such as whether it is the blood, or air, or fire with which we think. He also reports the view that it is the brain that furnishes the sensations of hearing, sight and smell. This corresponds very well with Alcmaeon's view of the brain as the central sensory organ and, although Alcmaeon is not mentioned by name, many scholars think that Plato must be referring to him here. Socrates connects this view of the brain with an empiricist epistemology, which Aristotle will later adopt (Posterior Analytics 100a3 ff.). This epistemology involves three steps: first, the brain provides the sensations of hearing, sight and smell, then, memory and opinion arise from these, and finally, when memory and opinion achieve fixity, knowledge arises. Some scholars suppose that this entire epistemology is Alcmaeon's (e.g., Barnes 1982, 149 ff.), while others more cautiously note that we only have explicit evidence that Alcmaeon took the first step (e.g., Vlastos 1970, 47, n.8).

2.3 Did Alcmaeon Practice Dissection?

Alcmaeon's empiricism has sometimes been thought to have arisen from his experience as a practicing physician (Guthrie 1962). He has also been hailed as the first to use dissection, but this is based on a hasty reading of the evidence. Calcidius, in his Latin commentary on Plato's Timaeus, praises Alcmaeon, along with Callisthenes and Herophilus, for having brought many things to light about the nature of the eye (A10). Most of what Calcidius goes on to describe, however, are the discoveries of Herophilus some two centuries after Alcmaeon (Lloyd 1975, Mansfeld 1975, Solmsen 1961). The only conclusions we can reasonably draw about Alcmaeon from the passage are that he excised the eyeball of an animal and observed poroi (channels, i.e. the optic nerve) leading from the eye in the direction of the brain (Lloyd 1975). Theophrastus' account of Alcmaeon's theory of sensation implies that he thought that there were such channels leading from each of the senses to the brain:

All the senses are connected in some way with the brain. As a result, they are incapacitated when it is disturbed or changes its place, for it then stops the channels, through which the senses operate. (A5)

There is no evidence, however, that Alcmaeon dissected the eye itself or that he dissected the skull in order to trace the optic nerve all the way to the brain. Alcmaeon's account of the other senses, far from suggesting that he carried out dissections in order to explain their function, implies that he did not (Lloyd 1975). Alcmaeon's conclusion that all of the senses are connected to the brain may have been drawn from nothing more that the excision of the eye and the general observation that the sense organs for sight, hearing, smell and taste are located on the head and appear connected to passages which lead inward towards the brain (Gomperz 1953, 69). It is striking in this regard that Alcmaeon gave no account of touch (A5), which is the only sense not specifically tied to the head. It would be a serious mistake then to say that Alcmaeon discovered dissection or that he was the father of anatomy, since there is no evidence that he used dissection systematically or even that he did more than excise a single eyeball.

2.4 Sense Preception

Theophrastus says that Alcmaeon did not explain sensation by the principle of like to like (i.e. by the likeness between the sense organ and what is perceived), a principle which was used by many early Greek thinkers (e.g., Empedocles). Unfortunately he gives no general account of how Alcmaeon did think sensation worked (A5). Alcmaeon explained each of the individual senses with the exception of touch, but these accounts are fairly rudimentary. He regarded the eye as composed of water and fire and vision as taking place when what is seen is reflected in the gleaming and translucent part of the eye. Hearing arises when an external sound is first transmitted to the outer ear and then picked up by the empty space (kenon) in the inner ear, which transmits it to the brain. Taste occurs through the tongue, which being warm and soft dissolves things with its heat and, because of its loose texture, receives and transmits the sensation. Smell is the simplest of all. It occurs "at the same time as we breathe in, thus bringing the breath to the brain" (A5).

2.5 The Immortality of the Soul

Alcmaeon developed the first argument for the immortality of the soul, but the testimonia concerning it differ slightly from one another, and it appears to have been taken over and developed by Plato, so that it is very hard to determine exactly how to reconstruct Alcmaeon's own argument. Barnes (1982, 116-120) provides the most insightful analysis. Alcmaeon appears to have started from the assumption that the soul is always in motion. At one extreme we might suppose that Alcmaeon only developed the crude argument from analogy, which Aristotle assigns to him (De An. 405a29). The soul is like the heavenly bodies, which Alcmaeon regarded as divine and immortal (A1, A12), in being always in motion, so it is also like them in being immortal. This is clearly fallacious, since it assumes that things that are alike in one respect will be alike in all others. The version in the doxographical tradition is somewhat better (A12). Alcmaeon thought that the soul moved itself in continual motion and was therefore immortal and like to the divine. The similarity to the divine is not part of the inference here but simply an illustrative comparison. The core of the argument is the necessary truth that what is always in motion must be immortal. This is the assumption from which Plato starts his argument for the immortality of the soul at Phaedrus 245c, but how much of Plato's analysis of what is always in motion can be assigned to Alcmaeon? Plato makes no mention of Alcmaeon in the passage. There are still serious questions for Alcmaeon, even on the more sophisticated version of the argument. We might well recognize that things with souls, i.e. things that are alive, are able to move themselves, and conclude that it is souls that bring this motion about. We might also conclude that the soul, as what moves something else, must be in motion itself (the synonymy principle of causation). But what sort of motion are we ascribing to souls and why should we think that it must be continual? The natural assumption might be that the soul's motion is thinking, but, at this early point in Greek thought, Alcmaeon was more likely to have thought that, if the soul is going to cause motion in space, it too must be in locomotion. Plato describes the soul as composed of two circles with contrary motions, which imitate the contrary motions of the fixed stars and the planets, so that the soul becomes a sort of orrery in the head (Timaeus 44d). It has been suggested that this image is borrowed from Alcmaeon (Barnes 1982, 118; Skemp 1942, 36 ff.).

Human beings perish because they are not able to join their beginning to their end.

At first sight, this assertion might appear to conflict with Alcmaeon's belief that the soul is immortal. It seems likely, however, that Alcmaeon distinguished between human beings as individual bodies, which do perish, and as souls, which do not (Barnes 1982, 115). There is no evidence about what Alcmaeon thought happened to the soul, when the body perished, however. He might have believed in reincarnation (along with the Pythagoreans), although his sharp distinction between animals and human beings may argue against this, or he might have thought that the soul joined other divine beings in the heavens. The point of Fragment 2 may be that, whereas the heavenly bodies do join their beginnings to their ends in circular motion, humans are not able to join their end in old age to their beginning in childhood, i.e. human life does not have a cyclical structure. We might even suppose that the soul tries to impose such a structure on the body from its own circular motion but ultimately fails (Guthrie 1962, 353).

3. Medical Doctrines

3.1 Health and Disease

Alcmaeon said that the equality (isonomia) of the powers (wet, dry, cold, hot, bitter, sweet, etc.) maintains health but that monarchy among them produces disease.

This is, in fact, not a fragment but a testimonium and most of the language comes from the doxographical tradition rather than Alcmaeon. The report goes on to say that Alcmaeon thought that disease arose because of an excess of heat or cold, which in turn arose because of an excess or deficiency in nutrition. Disease is said to arise in the blood, the marrow or the brain. It can also be caused by external factors such as the water, the locality, toil, or violence. The idea that health depends on a balance of opposed factors in the body is a commonplace in Greek medical writers. Although Alcmaeon is the earliest figure to whom such a conception of health is attributed, it may well be that he is not presenting an original thesis but rather drawing on the earlier medical tradition in Croton. Perhaps what is distinctive to Alcmaeon is the use of the specific political metaphor and terminology (isonomia, monarchia). Just as Anaximander explained the order of the cosmos in terms of justice in the city-state, so Alcmaeon used a political metaphor to explain the order of the human body. Although some have tried to find an application for isonomia in aristocratic politics, it is usually associated with the radical democracy which emerged in Athens in the late sixth century (Vlastos 1973, 175-7). Is Alcmaeon's use of the term simply descriptive of the equality of powers that is necessary for the healthy body, or does his use of the term to describe health suggest that he was in sympathy with radical democracy (Vlastos 1953, 363)?

3.2 Sleep, Embryology, and the Use of Analogy

Alcmaeon is the first to raise a series of questions in human and animal physiology that later become stock problems, which every thinker tries to address. He thus sets the initial agenda for Greek physiology (Longrigg 1993, 54-7; Lloyd 1966, 322 ff.). He said that sleep is produced by the withdrawal of the blood away from the surface of the body to the larger ("blood-flowing") vessels and that we awake when the blood diffuses throughout the body again (A18). Death occurs when the blood withdraws entirely. Hippocratic writers (Epid. VI 5.15) and Aristotle (H.A. 521a15) both seem to have adopted Alcmaeon's account of sleep. It is very unlikely, however, that Alcmaeon distinguished between veins (the "blood-flowing vessels") and arteries, as some have claimed. It is more likely that he simply distinguished between larger more interior blood vessels as opposed to smaller ones close to the surface (Lloyd 1991, 177). He probably argued that human seed was drawn from the brain (A13). Contrary to a popular Greek view, which regarded the father alone as providing seed, a view that would be followed by Aristotle (Lloyd 1983, 86 ff.), Alcmaeon argued that both parents contribute seed (A13) and that the child takes the sex of the parent who contributes the most seed (A14). According to one report, Alcmaeon thought that the head was the first part of the embryo to develop, although another report has him confessing that he did not have definite knowledge in this area, because no one is able to perceive what is formed first in the infant (A13). These reports are not inconsistent and conform to the epistemology with which Alcmaeon began his book. It is plausible to suppose that he regarded the development of the embryo as one of the imperceptibles about which we can have no certain knowledge. On the other hand, he may have regarded it as a reasonable inference that the part of the body which controls it in life, i.e. the brain, developed first in the womb. Dissection is of obvious relevance to the debate about the development of the embryo, and Alcmaeon's failure to appeal to dissection of animals in this case is further evidence that he did not employ it as a regular method (Lloyd 1979, 163). Alcmaeon studied not just humans but also animals and plants. He gave an explanation of the sterility of mules (B3) and, if we can believe Aristotle, thought that goats breathed through their ears (A7). More significantly, he used analogies with animals and plants in developing his accounts of human physiology. Thus, the pubic hair that develops when human males are about to produce seed for the first time at age fourteen is analogous to the flowering of plants before they produce seed (A15); milk in mammals is analogous to egg white in birds (A16). The infant in the womb absorbs nutrients through its entire body, like a sponge, although another report suggests that the embryo already feeds through its mouth (A17). However, the text of the latter report should perhaps be amended from stomati [mouth] to sômati [body], thus removing the contradiction (Olivieri 1919, 34). Analogies such as these will become a staple item in later Greek biological treatises, but Alcmaeon is one of the earliest figures in this tradition.

4. Cosmology

4.1 Astronomy

As indicated in section 1 above, there is considerable controversy as to whether and to what extent Alcmaeon was a typical Presocratic cosmologist. Certainly the evidence for his cosmology is meager. There are three references to his astronomical theory (A4). He is reported to have recognized that the planets have a motion from west to east opposite to the motion of the fixed stars. Some doubt that such knowledge was available at the beginning of the fifth century (Dicks 1970, 75). Others suggest that Anaximenes, in the second half of the sixth century, had already distinguished between the fixed stars, which are nailed to the ice-like vault of the sky, and planets which float on the air like leaves (DK13A7; Burkert 1972, 311). Alcmaeon's belief that the sun is flat is another possible connection to Anaximenes, who said that the sun was flat like a leaf (DK13A15). Finally, another similarity to Ionian astronomy is found in Alcmaeon's agreement with Heraclitus that lunar eclipses were to be explained by the turning of a bowl-shaped moon. One might have expected, however, that the moon would be flat like the sun (West 1971, 175).

4.2 Opposites

Did Alcmaeon present a cosmogony or cosmology in terms of the interaction of pairs of opposites? Such a cosmology could be seen as yet another connection to earlier speculation in Ionia, since Anaximander's cosmos is based on the "justice" established between conflicting opposites (DK12B1). Aristotle provides the primary evidence for such a cosmology (Metaph. 986a22 ff. = A3), but he compares Alcmaeon not to the Ionians but to a group of Pythagoreans who proposed a table of ten pairs of opposites. Alcmaeon agrees with these Pythagoreans in regarding the opposites as principles of things. Aristotle complains, however, that Alcmaeon did not arrive at a definite set of opposites but spoke haphazardly of white, black, sweet, bitter, good, bad, large and small, and only threw in vague comments about the remaining opposites. It may well be that Alcmaeon's primary discussion of opposites was in relation to his account of the human body (B4; see the discussion of his medical theories above). Aristotle's language supports this suggestion to some extent, when he summarizes Alcmaeon's view as that "the majority of human things (tôn anthrôpinôn) are in pairs" (Metaph. 986a31). Isocrates (A3) says that Alcmaeon, in contrast to Empedocles, who postulated four elements, said that there were only two, and, according to a heterodox view, Alcmaeon posited fire and earth as basic elements (Lebedev 1993). Most scholars follow Aristotle, however, in supposing that Alcmaeon thought that the human body and perhaps the cosmos is constituted from the balance of an indefinite number of opposites. Some have seen Alcmaeon's unwillingness to adopt a fixed set of opposites as a virtue and a further sign of his empiricism, which is willing to accept that the world is less tidy than theoretical constructs, such as the Pythagorean table of opposites, would suggest (Guthrie 1962, 346).

5. Importance and Influence

Alcmaeon has been somewhat neglected in recent scholarship on early Greek philosophy (e.g., he hardly appears in Long 1999 and Taylor 1997, the two most recent surveys of the subject). There would appear to be several reasons for this neglect. First, what remains of Alcmaeon's book has little to say on the metaphysical questions about the first principles of the cosmos and about being, which have dominated recent scholarship on the Presocratics. Second, doubts about his date and about the focus of his investigations have made it difficult to place him in the development of early Greek thought. Finally, a more accurate appreciation of his use of dissection has deflated some of the hyperbolic claims in earlier scholarship about his originality. The extent of his originality and the importance of his influence depend to a degree on his dating. An extremely late dating for his activity (after 450 BC) makes him appear to espouse the typical views of the age rather than to break new ground. If he was active in the early fifth century, his views are much more original. That Aristotle wrote a separate treatise in response to Alcmaeon argues in favor of his originality. He should probably be regarded as a pioneer in applying a political metaphor to the balance of opposites that constitute the healthy human body. The range of his work in biology is remarkable for the early fifth century and set the agenda for his successors. It is sometimes said that his conception of poroi (channels), which connect the sense organs to the brain, influenced Empedocles' theory of poroi, but the theories may share no more than the name. In Empedocles, all materials have pores in them, which determine whether they mix well with other objects. Sense organs also have pores, but these function not to connect the sense organ to the seat of intelligence (which for Empedocles is the heart) but to determine whether the sense organ can receive the effluences that are poured forth by external objects (Solmsen 1961, 157; Wright 1981, 230). Alcmaeon's influence was significant in three final ways: 1) His identification of the brain as the seat of human intelligence influenced Philolaus (B13), the Hippocratic Treatise, On the Sacred Disease, and Plato (Timaeus 44d), although a number of thinkers including Empedocles and Aristotle continued to regard the heart as the seat of perception and intelligence. 2) His empiricist epistemology may lie behind important passages in Plato (Phaedo 96b) and Aristotle (Posterior Analytics 100a). 3) He developed the first argument for the immortality of the soul, which influenced Plato's similar argument in the Phaedrus (245c ff.).

Bibliography

Texts and Commentaries

General Bibliography

Arthur Fairbanks, ed. and trans.
The First Philosophers of Greece
(London: K. Paul, Trench, Trubner, 1898), 157-234.

Hanover Historical Texts Project
Scanned and proofread by Aaron Gulyas, May 1998.
Proofread and pages added by Jonathan Perry, March 2001.

Fairbanks's Introduction

Empedokles, son of Meton, grandson of an Empedokles who was a victor at Olympia, made his home and Akragas in Sicily. he was born about 494 B.C., and lived to the age of sixty. The onle sure daye in his life is his visit to Thourioi soon after its foundation (444). Various stories are told of his political activity, which may be genuine traditions. At the same time he claimed almost the homage due to a god, and many miracles are attributed to him. His writings in some parts are said to imitate Orphic verses, and apparently his religious activity was in line with this sect. His death occured away from Sicily--probably in the Pelopnnesos.

Literature:-Sturz, Emped. vita et phil. carm. rell. Lips. 1805 ; Karsten, Emped. carm. rell. Amist. 1838 ; Bergk, kleine Schriften, Berl. 1839 ; Panzerbieter, Beitr. z. Kritik u. Erkl. d. Emped. Meining. 1844; Stein, Emped. Frag. Bonn 1852; Schneidewin, Philol. xv.; H. Diels; Hermes xv. pp. 161-179 ; Gorgias und Empedocles, Acad. Berol. 1884; Unger, Philol. Suppl. 1883, pp. 511-550; 0. Kern, Archiv f. d. Gesch. d. Philos. i. 498 ff.; Knatz, 'Eilipedoclea' in Schedae Phil. H. Usener oblatae, Bonn 1891 ; A. Platt, Journal of Philology, xxiv. p. 246 ; Bidez, Archiv, ix. 190 Gomperz, Hermes, xxxi. p. 469.

Translation of the Fragments: Book I

2. For scant means of acquiring knowledge are scattered among the members of the body; and many are the evils that break in to blunt the edge of studious thought. And gazing on a little portion of life that is not life, swift to meet their fate, they rise and are borne away like smoke, persuaded only of that on which each one chances as he is driven this way and that, but the whole he vainly boasts he has found. Thus these things are neither seen nor heard distinctly by men, nor comprehended by the mind. And thou, now that thou hast withdrawn hither, shalt learn no more than what mortal mind has seen.

11. But, ye gods, avert the madness of those men from my tongue, and from lips that are holy cause a pure stream to flow. And thee I pray, much-wooed whitearmed maiden Muse, in what things it is right for beings of a day to hear, do thou, and Piety, driving obedient car, conduct me on. Nor yet shall the flowers of honour [Page 161] well esteemed compel me to pluck them from mortal hands, on condition that I speak boldly more than is holy and only then sit on the heights of wisdom.

19. But come, examine by every means each thing how it is clear, neither putting greater faith in anything seen than in what is heard, nor in a thundering sound more than in the clear assertions of the tongue, nor keep from trusting any of the other members in which there lies means of knowledge, but know each thing in the way in which it is clear.

24. Cures for evils whatever there are, and protection against old age shalt thou learn, since for thee alone will I accomplish all these things. Thou shalt break the power of untiring gales which rising against the earth blow down the crops and destroy them; and, again, whenever thou wilt, thou shalt bring their blasts back; and thou shalt bring seasonable drought out of dark storm for men, and out of summer drought thou shalt bring streams pouring down from heaven to nurture the trees; and thou shalt lead out of Hades the spirit of a man that is dead.

33. Hear first the four roots of all things: bright Zeus, life-giving Hera (air), and Aidoneus (earth), and Nestis who moistens the springs of men with her tears. [Cf. Dox. p.99, n. 3.]

[Page 163] 36. And a second thing I will tell thee: There is no origination of anything that is mortal, nor yet any end in baneful death; but only mixture and separation of what is mixed, but men call this 'origination.'

40. But when light is mingled with air in human form, or in form like the race of wild beasts or of plants or of birds, then men say that these things have come into being; and when they are separated, they call them evil fate; this is the established practice, and I myself also call it so in accordance with the custom.

45. Fools! for they have no far-reaching studious thoughts who think that what was not before comes into being or that anything dies and perishes utterly.

48. For from what does not exist at all it is impossible that anything come into being, and it is neither possible nor perceivable that being should perish completely; for things will always stand wherever one in each case shall put them.

[Page 165] 51. A man of wise mind could not divine such things as these, that so long as men live what indeed they call life, so long they exist and share what is evil and what is excellent, but before they are formed and after they are dissolved, they are really nothing at all.

55. But for base men it is indeed possible to withhold belief from strong proofs ; but do thou learn as the pledges of our Muse bid thee, and lay open her word to the very core.

58. Joining one heading to another in discussion, not completing one path (of discourse) . . . for it is right to say what is excellent twice and even thrice.

60. Twofold is the truth I shall speak; for at one time there grew to be one alone out of many, and at another time, however, it separated so that there were many out of the one. Twofold is the coming into being, twofold the passing away, of perishable things; for the latter (i.e. passing away) the combining of [Page 167] all things both begets and destroys, and the former (i.e. coming into being), which was nurtured again out of parts that were being separated, is itself scattered.

66. And these (elements) never cease changing place continually, now being all united by Love into one, now each borne apart by the hatred engendered of Strife, until they are brought together in the unity of the all, and become subject to it. Thus inasmuch as one has been wont to arise out of many and again with the separation of the one the many arise, so things are continually coming into being and there is no fixed age for them; and farther inasmuch as they [the elements] never cease changing place continually, so they always exist within an immovable circle.

74. But come, hear my words, for truly learning causes the mind to grow. For as I said before in declaring the ends of my words: Twofold is the truth I shall speak; for at one time there grew to be the one

[Page 169] alone out of many, and at another time it separated so that there were many out of the one; fire and water and earth and boundless height of air, and baneful Strife apart from these, balancing each of them, and Love among them, their equal in length and breadth.

81. Upon her do thou gaze with thy mind, nor yet sit dazed in thine eyes; for she is wont to be implanted in men's members, and through her they have thoughts of love and accomplish deeds of union, and call her by the names of Delight, and Aphrodite; no mortal man has discerned her with them (the elements) as she moves on her way. But do thou listen to the undeceiving course of my words.[Cf. Parmenides v. 112]...

87. For these (elements) are equal, all of them, and of like ancient race; and one holds one office, another another, and each has his own nature. . . . For nothing is added to them, nor yet does anything pass away from them; for if they were continually perishing they would no longer exist. . . Neither is any part of this all empty, nor over full. For how should anything cause this all to increase, and whence should it come? And whither should they (the elements) perish, since no place is empty of them? And in their turn they prevail as the cycle comes round, and they disappear before.

[Page 171] each other, and they increase each in its allotted turn. But these (elements) are the same; and penetrating through each other they become one thing in one place and another in another, while ever they remain alike (i.e. the same).

110. For they two (Love and Strife) were before and shall be, nor yet, I think, will there ever be an unutterably long time without them both.

96. But come, gaze on the things that bear farther witness to my former words, if in what was said before there be anything defective in form. Behold the sun, warm and bright on all sides, and whatever is immortal and is bathed in its bright ray, and behold the rain-cloud, dark and cold on all sides; from the earth there proceed the foundations of things and solid bodies. In Strife all things are, endued with form and separate from each other, but they come together in Love and are desired by each other. 104. For from these (elements) come all things that are or have been or shall be; from these there grew up trees and men and women, wild beasts and birds and water-nourished fishes, and the very gods, long-lived, highest in honour.

121. And as when painters are preparing elaborate votive offerings-men well taught by wisdom in their [Page 173] art - they take many-coloured pigments to work with, and blend together harmoniously more of one and less of another till they produce likenesses of all things; so let not error overcome thy mind to make thee think there is any other source of mortal things that have likewise come into distinct existence in unspeakable numbers; but know these (elements), for thou didst hear from a god the account of them.

130. But come, I will tell thee now the first principle of the sun, even the sources of all things now visible, earth and billowy sea and damp mist and Titan aether (i.e. air) binding all things in its embrace.

135. Then neither is the bright orb of the sun greeted, nor yet either the shaggy might of earth or sea; thus, then, in the firm vessel of harmony is fixed God, a sphere, round, rejoicing in complete solitude.

[Page 175] 139. But when mighty Strife - was nurtured in its members and leaped up to honour at the completion of the time, which has been driven on by them both in turn under a mighty oath. . . .

146. If there were no limit to the depths of the earth and the abundant air, as is poured out in foolish words from the mouths of many mortals who see but little of the all.

154. A borrowed light, circular in form, it revolves about the earth, as if following the track of a chariot.

157. And she scatters his rays into the sky above, and spreads darkness over as much of the earth as the breadth of the gleaming-eyed moon.

166. But air1 sinks down beneath the earth with its long roots . . . . For thus it happened to be running at that time, but oftentimes otherwise.

169. But now I shall go back over the course of my verses, which I set out in order before, drawing my present discourse from that discourse. When Strife reached the lowest depth of the eddy and Love comes to be in the midst of the whirl, then all these things come together at this point so as to be one alone, yet not immediately, but joining together at their pleasure, one from one place, another from another. And as they were joining together Strife departed to the utmost boundary. But many things remained unmixed, [Page 181] alternating with those that were mixed, even as many as Strife, remaining aloft, still retained; for not yet had it entirely departed to the utmost boundaries of the circle, but some of its members were remaining within, and others had gone outside. 180. But, just as far as it is constantly rushing forth, just so far there ever kept coming in a gentle immortal stream of perfect Love; and all at once what before I learned were immortal were coming into being as mortal things,1 what before were unmixed as mixed, changing their courses. And as they (the elements) were mingled together there flowed forth the myriad species of mortal things, patterned in every sort of form, a wonder to behold.

186. For all things are united, themselves with parts of themselves - the beaming sun and earth and sky and sea - whatever things are friendly but have separated in mortal things. And so, in the same way, whatever things are the more adapted for mixing, these are loved by each other and made alike by Aphrodite. But what ever things are hostile are separated as far as possible from each other, both in their origin and in their mixing and in the forms impressed on them, absolutely unwonted to unite and very baneful, at the suggestion of Strife, since it has wrought their birth.

[Page 183] 195. In this way, by the good favour of Tyche, all things have power of thought.

197. For water is increased by water, primeval fire by fire, and earth causes its own substance to increase, and air, air.

199. And the kindly earth in its broad hollows received two out of the eight parts of bright Nestis, and four of Hephaistos, and they became white bones, fitted together marvellously by the glues of harmony.

203. And the earth met with these in almost equal amounts, with Hephaistos and Ombros and bright-shining Aether (i.e. air), being anchored in the perfect harbours of Kypris; either a little more earth, or a little less with more of the others. From these arose blood and various kinds of flesh.

Translation of the Fragments: Book II

[Page 185] 210. And if your faith be at all lacking in regard to these (elements), how from water and earth and air and sun (fire) when they are mixed, arose such colours and forms of mortal things, as many as now have arisen under the uniting power of Aphrodite.

215. And thus then Kypris, when she had moistened the earth with water, breathed air on it and gave it to swift fire to be hardened.

217. And all these things which were within were made dense, while those without were made rare, meeting with such moisture in the hands of Kypris.

222. For if thou shalt fix them in all thy close-knit mind and watch over them graciously with pure attention, all these things shall surely be thine for ever, and many others shalt thou possess from them. For these themselves shall cause each to grow into its own character, whatever is the nature1 of each. But if thou shalt reach out for things of another sort, as is the manner of men, there exist countless evils to blunt your studious thoughts; soon these latter shall cease to live as time goes on, desiring as they do to arrive at the longed-for generation of themselves. For know that all things have understanding and their share of intelligence.

233. This is in the heavy-backed shells found in the sea, of limpets and purple-fish and stone-covered tortoises. . . .there shalt thou see earth lying uppermost on the surface.

[Page 189] 236. Hair and leaves and thick feathers of birds are the same thing in origin, and reptiles' scales, too, on strong limbs.

244. Where many heads grew up without necks, and arms were wandering about naked, bereft of shoulders, and eyes roamed about alone with no foreheads.

247. This is indeed remarkable in the mass of human members; at one time all the limbs which form the body, united into one by Love, grow vigorously in the prime of life; but yet at another time, separated by evil Strife, they wander each in different directions along the breakers of the sea of life. Just so it is with [Page 191] plants and with fishes dwelling in watery halls, and beasts whose lair is in the mountains, and birds borne on wings.

254. But as divinity was mingled yet more with divinity, these things kept coming together in whatever way each might chance, and many others also in addition to these continually came into being.

257. Many creatures arose with double faces and double breasts, offspring of oxen with human faces, and again there sprang up children of men with oxen's heads; creatures, too, in which were mixed some parts from men and some of the nature of women, furnished with sterile members.

262. But come now, hear of these things; how fire separating caused the hidden offspring of men and weeping women to arise, for it is no tale apart from our subject, or witless. In the first place there sprang up out of the earth forms grown into one whole, having a share of both, of water and of fire. These in truth fire caused to grow up, desiring to reach its like; but they [Page 193] showed as yet no lovely body formed out of the members, nor voice nor limb such as is natural to men.

270. But the nature of the members (of the child?) is divided, part in the man's, part in the woman's (body).

273. It was poured out in the pure parts, and some meeting with cold became females.

276. In its warmer parts the womb is productive of the male, and on this account men are dark and more muscular and more hairy.

281. Knowing that there are exhalations from all things which came into existence.

281. Thus sweet was snatching sweet, and bitter darted to bitter, and sharp went to sharp, and hot coupled with hot.

[Page 195] 284. Water combines better with wine, but it is unwilling to combine with oil.

287. So all beings breathe in and out; all have bloodless tubes of flesh spread over the outside of the body, and at the openings of these the outer layers of skin are pierced all over with close-set ducts, so that the blood remains within, while a facile opening is cut for the air to pass through. Then whenever the soft blood speeds away from these, the air speeds bubbling in with impetuous wave, and whenever the blood leaps back the air is breathed out; as when a girl, playing with a klepsydra of shining brass, takes in her fair hand the narrow opening of the tube and dips it in the soft mass of silvery water, the water does not at once flow into the vessel, but the body of air within pressing on the close-set holes checks it till she uncovers the compressed stream; but then when the air gives way the determined amount of water enters. (302.) And so in the same way when the water occupies the depths of the bronze vessel, as long as the narrow opening and passage is blocked up by human flesh, the air outside striving eagerly to enter holds back the water inside behind the gates of the resounding tube, keeping control of its end, until she lets go with her hand.

[Page 197] (306.) Then, on the other hand, the very opposite takes place to what happened before; the determined amount of water runs off as the air enters Thus in the same way when the soft blood, surging violently through the members, rushes back into the interior, a swift stream of air comes in with hurrying wave, and whenever it (the blood) leaps back, the air is breathed out again in equal quantity.

314. So, then, all things have obtained their share of breathing and of smelling.

316. And as when one with a journey through a stormy night in prospect provides himself with a lamp and lights it at the bright-shining fire - with lanterns that drive back every sort of wind, for they scatter the breath of the winds as they blow - and the light darting out, inasmuch as it is finer (than the winds), shines across the threshold with untiring rays; so then elemental fire, shut up in membranes, it entraps in fine coverings to be the round pupil, and the coverings protect it against the deep water which flows about it, but the fire darting forth, inasmuch as it is finer. . . .

327. (The heart) lies in seas of blood which darts in opposite directions, and there most of all intelligence centres for men; for blood about the heart is intelligence in the case of men.

331. In so far as they change and become different, to this extent other sorts of things are ever present for them to think about.

333. For it is by earth that we see earth, and by water water, and by air glorious air; so, too, by fire we see destroying fire, and love by love, and strife by baneful strife. For out of these (elements) all things are fitted together and their form is fixed, and by these men think and feel both pleasure and pain.

Translation of the Fragments: Book III

[Page 201] 338. Would that in behalf of perishable beings thou, immortal Muse, mightest take thought at all for our thought to come by reason of our cares! Hear me now and be present again by my side, Kalliopeia, as I utter noble discourse about the blessed gods.

342. Blessed is he who has acquired a wealth of divine wisdom, but miserable he in whom there rests a dim opinion concerning the gods.

344. It is not possible to draw near (to god) even with the eyes, or to take hold of him with our hands, which in truth is the best highway of persuasion into the mind of man; for he has no human head fitted to a body, nor do two shoots branch out from the trunk, nor has he feet, nor swift legs, nor hairy parts, but he is sacred and ineffable mind alone, darting through the whole world with swift thoughts.

Translation of the Fragments: On Purifications

352. 0 friends, ye who inhabit the great city of sacred Akragas up to the acropolis, whose care is good deeds, who harbour strangers deserving of respect, who know not how to do baseness, hail! I go about among you an immortal god, no longer a mortal, honoured by all, as is fitting, crowned with fillets and luxuriant garlands. With these on my head, so soon as I come to flourishing cities I am reverenced by men and by women; and they follow after me in countless numbers, inquiring of me what is the way to gain, some in want of oracles, others of help in diseases, long time in truth pierced with grievous pains, they seek to hear from me keen-edged account of all sorts of things.

364. But why do I lay weight on these things, as though I were doing some great thing, if I be superior to mortal, perishing men?

[Page 205] 366. Friends, I know indeed when truth lies in the discourses that I utter; but truly the entrance of assurance into the mind of man is difficult and hindered by jealousy.

369. There is an utterance of Necessity, an ancient decree of the gods, eternal, sealed fast with broad oaths whenever any one defiles his body sinfully with bloody gore or perjures himself in regard to wrong-doing, one of those spirits who are heir to long life, thrice ten thousand seasons shall he wander apart from the blessed, being born meantime in all sorts of mortal forms, changing one bitter path of life for another. For mighty Air pursues him Seaward, and Sea spews him forth on the threshold of Earth, and Earth casts him into the rays of the unwearying Sun, and Sun into the eddies of Air; one receives him from the other, and all hate him. One of these now am I too, a fugitive from the gods and a wanderer, at the mercy of raging Strife.

383. For before this I was born once a boy, and a maiden, and a plant, and a bird, and a darting fish in the sea. 385. And I wept and shrieked on beholding the unwonted land where are Murder and Wrath, and other species of Fates, and wasting diseases, and putrefaction and fluxes.

390. From what honour and how great a degree of blessedness have I fallen here on the earth to consort with mortal beings!

393. Where were Chthonie and far-seeing Heliope (i.e. Earth and Sun?), bloody Contention and Harmony of sedate face, Beauty and Ugliness, Speed and Loitering, lovely Truth and dark-eyed Obscurity, Birth and Death, and Sleep and Waking, Motion and Stability, many-crowned Greatness and Lowness, and Silence and Voice.

400. Alas, ye wretched, ye unblessed race of mortal beings, of what strifes and of what groans were ye born!

404. For from being living he made them assume the form of death by a change. . . .

405. Nor had they any god Ares, nor Kydoimos (Uproar), nor king Zeus, nor Kronos, nor Poseidon, but queen Kypris. Her they worshipped with hallowed offerings, with painted figures, and perfumes of skilfully made odour, and sacrifices of unmixed myrrh and fragrant frankincense, casting on the ground libations from tawny bees. And her altar was not moistened with pure blood of bulls, but it was the greatest defilement among men, to deprive animals of life and to eat their goodly bodies.

[Page 211] 415. And there was among them a man of unusual knowledge, and master especially of all sorts of wise deeds, who in truth possessed greatest wealth of mind for whenever he reached out with all his mind, easily he beheld each one of all the things that are, even for ten and twenty generations of men.

421. For all were gentle and obedient toward men, both animals and birds, and they burned with kindly love; and trees grew with leaves and fruit ever on them, burdened with abundant fruit all the year.

425. This is not lawful for some and unlawful for others, but what is lawful for all extends on continuously through the wide-ruling air and the boundless light.

427. Will ye not cease from evil slaughter? See ye not that ye are devouring each other in heedlessness of mind?

430. A father takes up his dear son who has changed his form and slays him with a prayer, so great is his folly! They are borne along beseeching the sacrificer; but he does not hear their cries of reproach, but slays them and makes ready the evil feast. Then in the same manner son takes father and daughters their mother, and devour the dear flesh when they have deprived them of life.

436. Alas that no ruthless day destroyed me before I devised base deeds of devouring with the lips!

438. Among beasts they become lions haunting the mountains, whose couch is the ground, and among fair-foliaged trees they become laurels.

442. Compounding the water from five springs in unyielding brass, cleanse the hands.

445. Accordingly ye are frantic with evil hard to bear, nor ever shall ye ease your soul from bitter woes.

447. But at last are they prophets and hymn-writers and physicians and chieftains among men dwelling on the earth ; and from this they grow to be gods, receiving the greatest honours, sharing the same hearth with the other immortals, their table companions, free from human woes, beyond the power of death and harm.

Passages from Plato relating to Empedokles

Gorg. 493 A. And perhaps we really are dead, as I once before heard one of the wise men say: that now we are dead, and the body our tomb, and that that part of the soul, it so happens, in which desires are, is open to persuasion and moves upward and downward. And indeed a clever man-perbaps some inhabitant of Sicily or Italy-speaking allegorically, and taking the word from 'credible' and 'persuadable,' called it a jar. And those without intelligence he called uninitiated, and that part of the soul of the uninitiated where the desires are, lie called its intemperateness, and said it was not watertight, as a jar might be pierced with holes-using the simile because of its insatiate desires.

Meno 76 c. Do you say, with Empedokles, that there are certain effluences from things?-Certainly.

[Page 215] And that some of the effluences match certain of the pores, and others are smaller or larger ? - It is true.

And . . . colour is the effluence of forms in agreement with vision and perceptible by that sense?- It is.

Sophist. 24 D. And certain Ionian and Sicilian Muses agreed later that it is safest to weave together both opinions and to say that Being is many and one and that it is controlled by hate and love. Borne apart it is always borne together, say the more severe of the Muses. But the gentler concede that these things are always thus, and they say, in part, that sometimes all is one and rendered loving by Aphrodite, while at other times it is many and at enmity with itself by reason of a sort of strife.

Passages in Aristotle referring to Empedokles

Phys. i. 3 ; 187 a20. And others say that the opposites existing in the unity are separated out of it, as Anaximandros says, and as those say who hold that things are both one and many, as Empedokles and Anaxagoras.

i.4; 188 a 18. But it is better to assume elements fewer in number and limited, as Empedokles does.

ii. 4; 196 a 20. Empedokles says that the air is not always separated upwards, but as it happens.

viii. 1; 250 b 27. Empedokles says that things are in motion part of the time and again they are at rest; they are in motion when Love tends to make one out of many, or Strife tends to make many out of one, and in the intervening time they are at rest (Vv. 69-73).

viii. 1 ; 252 a 6. So it is necessary to consider this (motion) a first principle, which it seems Empedokles means in saying that of necessity Love and Strife control things and move them part of the time, and that they are at rest during the intervening time.

[Page 216] De Caelo 279 b 14. Some say that alternately at one time there is coming into being, at another time there is perishing, and that this always continues to be the case; so say Empedokles of Agrigentum and Herakleitos of Ephesus.

ii. 1 ; 284 a 24. Neither can we assume that it is after this manner nor that, getting a slower motion than its own downward momentum on account of rotation, it still is preserved so long a time, as Empedokles says.

ii. 13; 295 a 15. But they seek the cause why it remains, and some say after this manner, that its breadth or size is the cause; but others, as Empedokles, that the movement of the heavens revolving in a circle and moving more slowly, hinders the motion of the earth, like water in vessels.

iii. 2; 301 a 14. It is not right to make genesis take place out of what is separated and in motion. Wherefore Empedokles passes over genesis in the case of Love; for he could not put the heaven together preparing it out of parts that had been separated, and making the combination by means of Love; for the order of the elements has been established out of parts that had been separated, so that necessarily it arose out of what is one and compounded.

iii. 2; 302 a 28. Empedokles says that fire and earth and associated elements are the elements of bodies, and that all things are composed of these.

iii. 6; 305 a 1. But if separation shall in some way be stopped, either the body in which it is stopped will be indivisible, or being separable it is one that will never be divided, as Empedokles seems to mean.

iv. 2; 309 a 19. Some who deny that a void exists, do not define carefully light and heavy, as Anaxagoras and Empedokles.

[Page 217] Gen. corr. i. 1; 314 b 7. Wherefore Ernpedokles speaks after this manner, saying that nothing comes into being, but there is only mixture and separation of the mixed.

1.1 ; 315 a 3. Empedokles seemed both to contradict things as they appear, and to contradict himself. For at one time he says that no one of the elements arises from another, but that all other things arise from these; and at another time he brings all of nature together into one, except Strife, and says that each thing arises from the one.

1.8; 324 b 26. Some thought that each sense impression was received through certain pores from the last and strongest agent which entered, and they say that after this manner we see and hear and perceive by all the other senses, and further that we see through air and water and transparent substances because they have pores that are invisible by reason of their littleness, and are close together in series; and the more transparent substances have more pores. Many made definite statements after this manner in regard to certain things, as did Empedokles, not only in regard to active and passive bodies, but he also says that those bodies are mingled, the pores of which agree with each other. . . .

i.8; 325 a 34. From what is truly one multiplicity could not arise, nor yet could unity arise from what is truly manifold, for this is impossible ; but as Empedokles and some others say, beings are affected through pores, so all change and all happening arises after this manner, separation and destruction taking place through the void, and in like manner growth, solid bodies coming in gradually. For it is almost necessary for Empedokles to say as Leukippos does; for there are some solid and indivisible bodies, unless pores are absolutely contiguous.

325 b 19. But as for Empedokles, it is evident that he [Page 218] holds to genesis and destruction as far as the elements are concerned, but how the aggregate mass of these arises and perishes, it is not evident, nor is it possible for one to say who denies that there is an element of fire, and in like manner an element of each other thing-as Plato wrote in the Timaeos.

ii. 3 ; 330 b 19. And some say at once that there are four elements, as Empedokles. But lie combines them into two; for he sets all the rest over against fire.

ii. 6; 333 b 20. Strife then does not separate the elements, but Love separates those which in their origin are before god; and these are gods. Meteor. 357 a 24. In like manner it would be absurd if any one, saying that the sea is the sweat of the earth, thought he was saying anything distinct and clear, as for instance Empedokles; for such a statement might perhaps be sufficient for the purposes of poetry (for the metaphor is poetical), but not at all for the knowledge of nature.

369 b 11. Some say that fire originates in the clouds; and Empedokles says that this is what is encompassed by the rays of the sun.

De anim. I. 2; 404 b 7. As many as pay careful attention to the fact that what has soul is in motion, -these assume that soul is the most important source of motion; and as many as consider that it knows and perceives beings, these say that the first principle is soul, some making more than one first principle and others making one, as Empedokles says the first principle is the product of all the elements, and each of these is soul, saying (Vv. 333-335).

i. 4 ; 408 a 14. And in like manner it is strange that soul should be the cause of the mixture; for the mixture of the elements does not have the same cause as flesh and bone. The result then will be that there are many [Page 219] souls through the whole body, if all things arise out of the elements that have been mingled together; and the cause of the mixture is harmony and soul.

i. 5; 410 a 28. For it involves many perplexities to say, as Empedokles does, that each thing is known by the material elements, and like by like. . . And it turns out that Empedokles regards god as most lacking in the power of perception; for he alone does not know one of the elements, Strife, and (hence) all perishable things for each of these is from all (the elements).

ii.4 ; 415 b 28. And Empedokles was incorrect when he went on to say that plants grew downwards with their roots together because the earth goes in this direction naturally, and that they grew upwards because fire goes in this direction.

ii.7 ; 418 b 20 So it is evident that light is the presence of this (fire). And Empedokles was wrong, and any one else who may have agreed with him, in saying that the light moves and arises between earth and what surrounds the earth, though it escapes our notice.

De sens. 441 a 4. It is necessary that the water in it should have the form of a fluid that is invisible by reason of its smallness, as Empedokles says. 446 a 26. Empedokles says that the light from the sun first enters the intermediate space before it comes to vision or to the earth.

De respir. 477 a 32. Empedokles was incorrect in saying that the warmest animals having the most fire were aquatic, avoiding the excess of warmth in their nature, in order that since there was a lack of cold and wet in them, they might be preserved by their position.

Pneumat. 482 a 29. With reference to breathing some do not say what it is for, but only describe the manner in which it takes place, as Empedokles and Demokritos.

[Page 220] 484 a 38. Empedokles says that fingernails arise from sinew by hardening.

Part. anim. i. 1 ; 640 a 19. So Empedokles was wrong in saying that many characteristics appear in animals because it happened to be thus in their birth, as that they have such a spine because they happen to be descended from one that bent itself back. . .

i. 1 ; 642 a 18. And from time to time Empedokles chances on this, guided by the truth itself, and is compelled to say that being and nature are reason, just as when he is declaring what a bone is; for he does not say it is one of the elements, nor two or three, nor all of them, but it is the reason of the mixture of these.

De Plant. i.; 815 a 16. Anaxagoras and Empedokles say that plants are moved by desire, and assert that they have perception and feel pleasure and pain. . . .Empedokles thought that sex had been mixed in them. (Note 817 a 1, 10, and 36.)

i. ; 815 b 12. Empedokles et al. said that plants have intelligence and knowledge.

i. ; 817 b 35. Empedokles said again that plants have their birth in an inferior world which is not perfect in its fulfilment, and that when it is fulfilled an animal is generated.

i. 3; 984 a 8. Empedokles assumes four elements, adding earth as a fourth to those that have been mentioned; for these always abide and do not come into being, but in greatness and smallness they are compounded and separated out of one and into one.

i. 3; 984 b 32. And since the opposite to the good appeared to exist in nature, and not only order and beauty but also disorder and ugliness, and the bad appeared to be more than the good and the ugly more than the beautiful, so some one else introduced Love and Strife, each the cause of one of these. For if one were to [Page 221] follow and make the assumption in accordance with reason and not in accordance with what Empedokles foolishly says, he will find Love to be the cause of what is good, and Strife of what is bad; so that if one were to say that Empedokles spoke after a certain manner and was the first to call the bad and the good first principles, perhaps he would speak rightly, if the good itself were the cause of all good things, and the bad of all bad things.

Met. i. 4; 915 a 21. And Empedokles makes more use of causes than Anaxagoras, but not indeed sufficiently; nor does he find in them what has been agreed upon. At any rate love for him is often a separating cause and strife a uniting cause. For whenever the all is separated into the elements by strife, fire and each of the other elements are collected into one; and again, whenever they all are brought together into one by love, parts are necessarily separated again from each thing. Empedokles moreover differed from those who went before, in that he discriminated this cause and introduced it, not maknig the cause of motion one, but different and opposite. Further, he first described the four elements spoken of as in the form of matter; but he did not use them as four but only as two, fire by itself, and the rest opposed to fire as being one in nature, earth and air and water.

1.8; 989 a 20. And the same thing is true if one asserts that these are more numerous than one, as Empedokles says that matter is four substances. For it is necessary that the same peculiar results should hold good with reference to him. For we see the elements arising from each other inasmuch as fire and earth do not continue the same substance (for so it is said of them in - the verses on nature) ; and with reference to the cause of their motion, whether it is necessary to assume one or two, we must think that he certainly did not speak either in a correct or praiseworthy manner.

[Page 222] 1.9; 993 a 15. For the first philosophy seems to speak inarticulately in regard to all things, as though it were childish in its causes and first principle, when even Empedokles says that a bone exists by reason, that is, that it was what it was and what the essence of the matter was. Meta. ii. 4 ; 1000 a 25. And Empedokles who, one might think, spoke most consistently, even he had the same experience, for he asserts that a certain first principle, Strife, is the cause of destruction; but one might think none the less that even this causes generation out of the unity; for all other things are from this as their source, except god.

Meta. ii. 4; 1000 a 32. And apart from these verses (vv. 104-107) it would be evident, for if strife were not existing in things, all would be one, as lie says; for when they come together, strife comes to a stand last of all. Wherefore it results that for him the most blessed God has less intelligence than other beings; for he does not know all the elements; for he does not have strife, and knowledge of the like is by the like. Meta. ii. 4; 1000 b 16. He does not make clear any cause of necessity. But, nevertheless, he says thus much alone consistently, for he does not make some beings perishable and others imperishable, but he makes all perishable except the elements. And the problem now under discussion is why some things exist and others do not, if they are from the same (elements). Meta. xi. 10; 1075 b 2. And Empedokles speaks in a manner, for he makes friendship the good. And this is the first principle, both as the moving cause, for it brings things together ; and as matter, for it is part of the mixture.

Ethic. vii. 5 ; 1147 b 12. He has the power to speak [Page 223] but not to understand, as a drunken man repeating verses of Empedokles. Ethic. viii. 2 ; 1155 b 7. Others, including Empedokles, say the opposite, that the like seeks the like.

Moral. ii. 11 ; 1208 b 11. And he says that when a dog was accustomed always to sleep on the same tile, Empedokles was asked why the dog always sleeps on the same tile, and he answered that the dog had some likeness to the tile, so that the likeness is the reason for its frequenting it.

Poet. 1; 1447 b 16. Homer and Empedokles have nothing in common but the metre, so that the former should be called a poet, the latter should rather be called a student of nature.

Fr. 65; Diog. Laer. viii. 57. Aristotle, in the Sophist, says that Empedokles first discovered rhetoric and Zeon dialectic.

Fr. 66; Diog. Laer. viii. 63. Aristotle says that Empedokles) became free and estranged from every form of rule, if indeed he refused the royal power that was granted to him, as Xanthos says in his account of him, evidently much preferring his simplicity.

Passages in Diels' 'Doxographi Graeci' relating to Empedokles

Aet. Plac. i. 3; Dox. 287. Empedokles of Akragas, son of Meton, says that there are four elements, fire, air, water, earth; and two dynamic first principles, love and strife; one of these tends to unite, the other to separate. And he speaks as follows: -Hear first the four roots of all things, bright Zeus and life-bearing Hera and Aidoneus, and Nestis, who moistens the springs of men with her tears. Now by Zeus he means the seething and the aether, by life-bearing Hera the moist air, [Page 224] and by Aidoneus the earth; and by Nestis, spring of men, he means as it were moist seed and water.

i. 4 ; 291. Empedokles: The universe is one; not however that the universe is the all, but some little part of the all, and the rest is matter. i. 7 ; 303. And he holds that the one is necessity, and that its matter consists of the four elements, and its forms are strife and love. And he calls the elements gods, and the mixture of these the universe. And its uniformity will be resolved into them;1 and he thinks souls are divine, and that pure men who in a pure way have a share of them (the elements) are divine. i. 13; 312. Empedokles: Back of the four elements there are smallest particles, as it were elements before elements, homoeomeries (that is, rounded bits). i. 15; 313. Empedokles declared that colour is the harmonious agreement of vision with the pores. And there are four equivalents of the elements -- white, black, red, yellow. i. 16; 315. Empedokles (and Xenokrates): The elements are composed of very small masses which are the most minute possible, and as it were elements of elements. i. 24; 320. Empedokles et al. and all who make the universe by putting together bodies of small parts, introduce combinations and separations, but not genesis and destruction absolutely; for these changes take place not in respect to quality by transformation, but in respect to quantity by putting together. i. 26 ; 321. Empedokles: The essence of necessity is the effective cause of the first principles and of the elements.

Act. Plac. ii. 1 ; Dox. 328. Empedokles: The course of the sun is the outline of the limit of the universe. ii. 4 ; 331. Empedokles The universe perishes according to the alternating rule of Love and Strife. ii. 6 ; 334. Empedokles: The aether was first separated, and secondly fire, and then earth, from which, [Page 225] as it was compressed tightly by the force of its rotation, water gushed forth; and from this the air arose as vapour, and the heavens arose from the aether, the sun from the fire, and bodies on the earth were compressed out of the others. ii. 7 ; 336. Empedokles : Things are not in fixed position throughout the all, nor yet are the places of the elements defined, but all things partake of one another. ii. 8 ; 338. Empedokles : When the air gives way at the rapid motion of the sun, the north pole is bent so that the regions of the north are elevated and the legions of the south depressed in respect to the whole universe. 11.10; 339. Empedokles : The right side is toward the summer solstice, and the left toward the winter solstice. ii. 11 ; 339. Empedokles : The heaven is solidified from air that is fixed in crystalline form by fire, and embraces what partakes of the nature of fire and of the nature of air in each of the hemispheres. ii. 13 ; 341. Empedokles The stars are fiery bodies formed of fiery matter, which the air embracing in itself pressed forth at the first separation. 342. The fixed stars are bound up with the crystalline (vault), but the planets are set free. ii. 20; 350. Empedokles There are two suns; the one is the archetype, fire in the one hemisphere of the universe, which has filled that hemisphere, always set facing the brightness which corresponds to itself; the other is the sun that appears, the corresponding brightness in the other hemisphere that has been filled with air mixed with heat, becoming the crystalline sun by reflection from the rounded earth, and dragged along with the motion of the fiery hemisphere; to speak briefly, the sun is the brightness corresponding to the fire that surrounds the earth. ii. 21 ; 351. The sun which faces the opposite brightness, is of the same size as the earth. ii. 23; 353. Empedokles The solstices are due to the fact that the sun is hindered from moving [Page 226] always in a straight line by the sphere enclosing it, and by the tropic circles. ii. 24; 354. The sun is eclipsed when the moon passes before it. ii. 25; 357. Empedokles : The moon is air rolled together, cloudlike, its fixed form due to fire, so that it is a mixture. ii. 27; 358. The moon has the form of a disk. ii. 28; 358. The moon has its light from the sun. ii. 31 ; 362. Empedokles : The moon is twice as far from the sun as it is from the earth (?) 363. The distance across the heavens is greater than the height from earth to heaven5 which is the distance of the moon from us; according to this the heaven is more spread out, because the universe is disposed in the shape of an egg.

Aet. Plac. iii. 3; Dox. 368. Empedokles: (Thunder and lightning are) the impact of light on a cloud so that the light thrusts out the air which hinders it; the extinguishing of the light and the breaking up of the cloud produces a crash, and the kindling of it produces lightning, and the thunderbolt is the sound of the lightning. iii.8; 375. Empedokles and the Stoics : Winter comes when the air is master, being forced up by condensation; and summer when fire is master, when it is forced downwards. iii. 16 ; 381. The sea is the sweat of the earth, brought out by the heat of the sun on account of increased pressure.

Aet. Plac. iv. 3; Theod. v.18; Dox. 389. Empedokles: The soul is a mixture of what is air and aether in essence. iv. 5 ; 392. Empedokles et al. : Mind and soul are the same, so that in their opinion no animal would be absolutely devoid of reason. Theod. v.23; 392. Empedokles et al.: The soul is imperishable. Aet. iv. 9; 396. Empedokles et al. : Sensations are deceptive. 397. Sensations arise part by part according to the symmetry of the pores, each particular object of sense being adapted to some sense (organ). iv. 13; 403. [Page 227] Empedokles: Vision receives impressions both by means of rays and by means of images. But more by the second method; for it receives effluences. iv. 14 ; 405. (Reflections from mirrors) take place by means of effluences that arise on the surface of the mirror, and they are completed by means of the fiery matter that is separated from the mirror, and that bears along the air which lies before them into which the streams flow. iv. 6 ; 406 Empedokles : Hearing takes place by the impact of wind on the cartilage of the ear, which, he says, is hung up inside the ear so as to swing and be struck after the manner of a bell. iv. 17 ; 407. Empedokles : Smelt is introduced with breathings of the lungs; whenever the breathing becomes heavy, it does not join in the perception on account of roughness, as in the case of those who suffer from a flux. iv 22; 411. Empedokles : The first breath of the animal takes place when the moisture in infants gives way, and the outside air comes to the void to enter the opening of the lungs at the side; and after this the implanted warmth at the onset from without presses out from below the airy matter, the breathing out; and at the corresponding return into the outer air it occasions a corresponding entering of the air, the breathing in. And that which now controls the blood as it goes to the surface and as it presses out the airy matter through the nostrils by its own currents on its outward passage, becomes the breathing out; and when the air runs back and enters into the fine openings that are scattered through the blood, it is tile breathing in. And he mentions the instance of the clepsydra.

Aet. Plac. v.7; 419. Empedokles: Male or female are born according to warmth and coldness; whence he records that the first males were born to the east and south from the earth, and the females to the north. v.8; 420. Empedokles: Monstrosities are due to too much or [Page 228] too little seed (semen), or to disturbance of motion, or to division into several parts, or to a bending aside. V. 10; 421. Empedokles: Twins and triplets are due to excess of seed and division of it. v.11 ; 422. Empedokles: Likenesses (of children to parents) are due to power of the fruitful seed, and differences occur when the warmth in the seed is dissipated.1 v.12; 423. Empedokles: Offspring are formed according to the fancy of the woman at the time of conception; for oftentimes women fall in love with images and statues, and bring forth offspring like these. v. 14; 425. Empedokles: (Mules are not fertile) because the womb is small and low and narrow, and attached to the belly in a reverse manner, so that the seed does not go into it straight, nor would it receive the seed even if it should reach it. v. 15; 425. Empedokles: The embryo is [not] alive, but exists without breathing in the belly; and the first breath of the animal takes place at birth, when the moisture in infants gives way, and when the airy matter from without comes to the void, to enter into the openings of the lungs. v.19 ; 430. Empedokles : The first generations of animals and plants were never complete, but were yoked with incongruous parts ; and the second were forms of parts that belong together; and the third, of parts grown into one whole; and the fourth were no longer from like parts, as for instance from earth and water, but from elements already permeating each other; for sonic the food being condensed, for others the fairness of the females causmg an excit~ent of the motion of the seed. And the classes of all the animals were separated on account of such mixings; those more adapted to the water rushed into this, others sailed up into the air as many as had the more of fiery matter, and the heavier remained on the earth, and equal portions in the mixture spoke in [Page 229] the breasts of all. V. 22; 434. Empedokles : Flesh is the product of equal parts of the four elements mixed together, and sinews of double portions of fire and earth mixed together, and the claws of animals are the product of sinews chilled by contact with the air, and bones of two equal parts of water and of earth and four parts of fire mingled together. And sweat and tears come from blood as it wastes away, and flows out because it has become rarefied. v.24; 435. Empedokles: Sleep is a moderate cooling of the warmth in the blood, death a complete cooling. v.25 ; 437. Empedokles Death is a separation of the fiery matter out of the mixture of which the man is composed; so that from this standpoint death of the body and of the soul happens together; and sleep is a separating of the fiery matter. v.26; 438. Empedokles : Trees first of living beings sprang from the earth, before the sun was unfolded in the heavens and before day and night were separated; and by reason of the symmetry of their mixture they contain the principle of male and female; and they grow, being raised by the warmth that is in the earth, so that they are parts of the earth, just as the fetus in the belly is part of the womb; and the fruits are secretions of the water and fire in the plants; and those which lack (sufficient) moisture shed their leaves in summmer when it is evaporated, but those which have more moisture keep their leaves, as in the case of the laurel and the olive and the date-palm; and differences in their juices are (due to) variations in the number of their component parts, and the differences in plants arise because they derive their homoeomeries from (the earth which) nourishes them, as in the case of grape-vines; for it is not the kind of vine which makes wine good, but the kind of soil which nurtures it. v.26; 440: Empedokles: Animals are nurtured by the substance of what is akin to them [moisture], and [Page 230] they grow with the presence of warmth, and grow smaller and die when either of these is absent; and men of the present time, as compared with the first living beings, have been reduced to the size of infants (?). v. 28; 440. Empedokles: Desires arise in animals from a lack of the elements that would render each one complete, and pleasures. . .

Theophr. Phys. Opin. 3; Dox. 478. Empedokles of Agrigentum makes the material elements four fire and air and water and earth, all of them eternal, and changing in amount and smallness by composition and separation; and the absolute first principles by which these four are set in motion, are Love and Strife; for the elements must continue to be moved in turn, at one time being brought together by Love and at another separated by Strife; so that in his view there are six first principles; for sometimes he gives the active power to Love and Strife, when he says (vv. 67-68): 'Now being all united by Love into one, now each borne apart by hatred engendered of Strife;' and again he ranks these as elements along with the four when he says (vv. 77-80): 'And at another time it separated so that there were many out of the one; fire and water and earth and boundless height of air, and baneful Strife apart from these, balancing each of them, and Love among them, their equal in length and breadth.'

Fr. 23; Dox. 495. Some say that the sea is as it were a sort of sweat from the earth; for when the earth is warmed by the sun it gives forth moisture; accordingly it is salt, for sweat is salt. Such was the opinion of Empedokles.

Theophr. de sens. 7; Dox. 500. Empedokles speaks in like manner concerning all the senses, and says that we perceive by a fitting into the pores of each sense. So they [Page 231] are not able to discern one another's objects, for the pores of some are too wide and of others too narrow for the object of sensation, so that some things go right through untouched, and others are unable to enter completely. And he attempts to describe what vision is; and lie says that what is in the eye is fire and water, and what surrounds it is earth and air, through which light being fine enters, as the light in lanterns. Pores of fire and water are set alternately, and the fire-pores recognise white objects, the water-pores black objects; for the colours harmonise with the pores. And the colours move into vision by means of effluences. And they are not composed alike . . . and some of opposite elements; for some the fire is within and for others it is on the out-side, so some animals see better in the daytime and others at night; those that have less fire see better by day, for the light inside them is balanced by the light outside them; and those that have less water see better at night, for what is lacking is made up for them. And in the opposite case the contrary is true; for those that have the more fire are dim-sighted, since the fire increasing plasters up and covers the pores of water in the daytime; and for those that have water in excess, the same thing happens at night; for the fire is covered up by the water. . . Until in the case of some the water is separated by the outside light, and in the case of others the fire by the air; for the cure of each is its opposite. That which is composed of both in equal parts is the best tempered and most excellent vision. This, approximately, is what he says concerning vision. And hearing is the result of noise coming from outside. For when (the air) is set in motion by a sound, there is an echo within; for the hearing is as it were a bell echoing within, and the ear he calls an 'offshoot of flesh' (v.315): and the air when it is set [Page 232] in motion strikes on something hard and makes an echo.1 And smell is connected with breathing, so those have the keenest smell whose breath moves most quickly; and the strongest odour arises as an effluence from fine and light bodies. But he makes no careful discrimination with reference to taste and touch separately, either how or by what means they take place, except the general statement that sensation takes place by a fitting into the pores ; and pleasure is due to likenesses in the elements and in their mixture, and pain to the opposite. And he speaks similarly concerning thought and ignorance : Thinking is by what is like, and not perceiving is by what is unlike, since thought is the same thing as, or something like, sensation. For recounting how we recognise each thing by each, he said at length (vv. 336-337): Now out of those (elements) all things are fitted together and their form is fixed, and by these men think and feel pleasure and pain. So it is by blood especially that we think; for in this especially are mingled the elements of things. And those in whom equal and like parts have been mixed, not too far apart, nor yet small parts, nor exceeding great, these have the most intelligence and the most accurate senses; and those who approximate to this come next; and those who have the opposite qualities are the most lacking in intelligence. And those in whom the elements are scattered and rarefied, are torpid and easily fatigued; and those in whom the elements are small and thrown close together, move so rapidly and meet with so many things that they accomplish but little by reason of the swiftness of the motion of the blood. And those in whom there is a well-tempered mixture in some one part, are wise at this point; so some are good orators, others good artisans, according as the mixture is in the [Page 233] hands or in the tongue; and the same is true of the other powers.

Theophr. de sens. 59 ; Dox. 516. And Empedokles says of colours that white is due to fire, and black to water.

Cic. De nat. deor. xii.; Dox. Empedokles, along with many other mistakes, makes his worst error in his conception of the gods. For the four beings of which he holds that all things consist, he considers divine; but it is clear that these are born and die and are devoid of all sense. Hipp. Phil. 3 ; Dox. 558. And Empedokles, who lived later, said much concerning the nature of the divinities, how they live in great numbers beneath the earth and manage things there. He said that Love and Strife were the first principle of the all, and that the intelligent fire of the monad is god, and that all things are formed from fire and are resolved into fire; and the Stoics agree closely with his teaching, in that they expect a general conflagration. And he believed most fully in transmigration, for he said : 'For in truth I was born a boy and a maiden, and a plant and a bird, and a fish whose course lies in the sea.' He said that all souls went at death into all sorts of animals.

Plut. Strom. 10; Dox. 582. Empedokles of Agrigentum: The elements are four--fire, water, aether, earth. And the cause of these is Love and Strife. From the first mixture of the elements he says that the air was separated and poured around in a circle; and after the air the fire ran off, and not having any other place to go to, it ran up from under the ice that was around the air. And there are two hemispheres moving in a circle around the earth, the one of pure fire, the other of air and a little fire mixed, which lie thinks is night. And motion [Page 234] began as a result of the weight of the fire when it was collected. And the sun is not fire in its nature, but a reflection of fire, like that which takes place in water. And he says the moon consists of air that has been shut up by fire, for this becomes solid like hail; and its light it gets from the sun. The ruling part; is not in the head or in the breast, but in the blood; wherefore in whatever part of the body the more of this is spread, in that part men excel.

Epiph. adv. Haer. iii. 19; Dox. 591. Empedokles of Agrigentum, son of Meton, regarded fire and earth and water and air as the four first elements, and he said that enmity is the first of the elements. For, he says, they were separated at first, but now they are united into one, becoming loved by each other. So in his view the first principles and powers are two, Enmity and Love, of which the one tends to bring things together and the other to separate them.

Fairbanks's Introduction

[Page 235] Anaxagoras of Klazomenae, son of Hegesiboulos, was born in the seventh Olympiad (500-497) and died in the first year of the eighty-eighth Olympiad (428), according to the chronicles of Apollodoros. it is said that he neglected his possessions in his pursuit of philosophy; he began to teach philosophy in the archonship of Kallias at Athens (480). The fall of metoeoric stone at Aegos Potamoi (467 or 469) influenced profoundly his views of the heavenly bodies. Perikles brought him to Athens, and tradition says he remained there thirty years. His exile (434-432) was brought about by enemies of Perikles, and he died at Lampsakos. He wrote but one book, according to Diogenes, and the same authority says this was written in a pleasing and lofty style.

The Fragments of Anaxagoras

1. All things were together, infinite both in number and in smallness; for the small also was infinite. And when they were all together, nothing was clear and distinct because of their smallness; for air and aether comprehended all things, both being infinite; for these are present in everything, and are greatest both as to number and as to greatness.

2. For air and aether are separated from the surrounding mass; and the surrounding (mass) is infinite in quantity.

4. But before these were separated, when all things were together, not even was any colour clear and distinct for the mixture of all things prevented it, the mixture of moist and dry, of the warm and the cold, and of the bright and the dark (since much earth was present), and of germs infinite in number, in no way like each other; for none of the other things at all resembles the one the other.

3. And since these things are so, it is necessary to think that in all the objects that are compound there existed many things of all sorts, and germs of all objects, having all sorts of forms and colours and tastes.

[Page 239] 10. And men were constituted, and the other animals, as many as have life. And the men have inhabited cities and works constructed as among us, and they have sun and moon and other things as among us; and the earth brings forth for them many things of all sorts, of which they carry the most serviceable into the house and use them. These things then I have said concerning the separation, that not only among us would the separation take place, but elsewhere too.

11. So these things rotate and are separated by force and swiftness. And the swiftness produces force; and their swiftness is in no way like the swiftness of the things now existing among men, but it is certainly many times as swift.

14. When they are thus distinguished, it is necessary to recognise that they all become no fewer and no more. For it is impossible that more than all should exist, but all are always equal.

5. In all things there is a portion of everything except mind; and there are things in which there is mind also.

6. Other things include a portion of everything, but mind is infinite and self-powerful and mixed with nothing, but it exists alone itself by itself. For if it were [Page 241] not by itself, but were mixed with anything else, it would include parts of all things, if it were mixed with any thing; for a portion of everything exists in everything, as has been said by me before, and things mingled with it would prevent it from having power over anything in the same way that it does now that it is alone by itself. For it is the most rarefied of all things and the purest, and it has all knowledge in regard to everything and the greatest power; over all that has life, both greater and less, mind rules. And mind ruled the rotation of the whole, so that it set it in rotation in the beginning. First it began the rotation from a small beginning, then more and more was included in the motion, and yet more will be included. Both the mixed and the separated and distinct, all things mind recognised. And whatever things were to be, and whatever things were, as many as are now, and whatever things shall be, all these mind arranged in order; and it arranged that rotation, according to which now rotate stars and sun and moon and air and aether, now that they are separated. Rotation itself caused the separation, and the dense is separated from the rare, the warm from the cold, the bright from the dark, the dry from the moist. And there are many portions of many things. Nothing is absolutely separated nor distinct, one thing from another, except mind. All mind is of like character, both the greater and the smaller. But nothing different is like anything else, but [Page 243] in whatever object there are the most, each single object is and was most distinctly these things.[1]

7. And when mind began to set things in motion, there was separation from everything that was in motion, and however much mind set in motion, all this was made distinct. The rotation of the things that were moved and made distinct caused them to be yet more distinct.

8. The dense, the moist, the cold, the dark, collected there where now is the earth; the rare, the warm, the dry, the bright, departed toward the farther part of the aether.

9. Earth is condensed out of these things that are separated. For water is separated from the clouds, and earth from the water; and from the earth stones are condensed by cold; and these are separated farther from water.[2]

12. But mind, as it always has been, especially now also is where all other things are, in the surrounding mass, and in the things that were separated, and in the things that are being separated.

13. Things in the one universe are not divided from each other, nor yet are they cut off with an axe, neither hot from cold, nor cold from hot.

15. For neither is there a least of what is small, but there is always a less. For being is not non-being. [Page 245] But there is always a greater than what is great. And it is equal to the small in number; but with reference to itself each thing is both small and great.

16. And since the portions of the great and the small are equal in number, thus also all things would be in everything. Nor yet is it possible for them to exist apart, but all things include a portion of everything. Since it is not possible for the least to exist, nothing could be separated, nor yet could it come into being of itself, but as they were in the beginning so they are now, all things together. And there are many things in all things, and of those that are separated there are things equal in number in the greater and the lesser.

17. The Greeks do not rightly use the terms 'coming into being' and 'perishing.' For nothing comes into being nor yet does anything perish, but there is mixture and separation of things that are. So they would do right in calling the coming into being 'mixture,' and the perishing 'separation.'

18. For how could hair come from what is not hair? Or flesh from what is not flesh?

Ancient Authors' Commentaries on Anaxagoras

Literature:--Shaubach, Anax. Claz. Frag. Lips. 1827; W. Schorn, Anax. Claz. et Diog. Apoll. Frag. Bonn 1829; Panzerbieter, De frag. Anax. ord. Meining. 1936; Fr. Breier, Die Philosophie des Anax. nach Arist. Berl. 1840. Cf. Diels, Hermes xiii. 4.

Apol. 26 D. He asserts that I say the sun is a stone and the moon is earth. Do you think of accusing Anaxagoras, Meletos, and have you so low an opinion of these men and think them so unskilled in letters as not to know that the books of Anaxagoras of Klazomenae are full of these doctrines? And forsooth the young men are learning these matters from me, which sometimes they can buy from the orchestra for a drachma at the most, and laugh at Sokrates if he pretends that they are his particularly seeing they are so strange. [Page 246] Phaedo 72 c. And if all things were composite and were not separated, speedily the statement of Anaxagoras would become true, 'All things were together.'

97 C. I heard a man reading from a book of one Anaxagoras (he said), to the effect that it is mind which arranges all things and is the cause of all things.

98 B. Reading the book, I see that the man does not make any use of mind, nor does he assign any causes for the arrangement of things, but he treats air and aether and water as causes, and many other strange things.

Lysis 214 B. The writings of the wisest men say... that it is necessary for the like always to be loved by the unlike.

Hipp. Mai. 283 A. They say you had an experience opposite to that of Anaxagoras; for though he inherited much property he lost it all by his carelessness; so he practised a senseless wisdom.

Kratyl. 400 A. And do you not believe Anaxagoras that the nature of all other things is mind, and that it is soul which arranges and controls them? (cf. Phaedo 72 c).

409 A. It looks as though the opinion Anaxagoras recently expressed was a more ancient matter, that the moon has its light from the sun.

413 C. Anaxagoras is right in saying that this is mind, for he says that mind exercising absolute power and mingled with nothing disposes all things, running through all

Riva1. 132 A. But the youths seemed to be quarrelling about Anaxagoras or Oenopedos, for they were evidently drawing circles and imitating certain inclinations by the slope of their hands with great earnestness.

Phil. 28 c. All the wise men agree that mind is king of heaven and earth for us. [Page 247] 30 D. Some long ago declared that always mind rules the all.

Legg. 967 B. And some had the daring to conjecture this very thing, saying that it is mind which disposes all things in the heavens. And the same men again, being in error as to the nature of soul, in that it is older than bodies, while they regarded it as younger, to put it in a word, turned all things upside down, and themselves most of all. For indeed all things before their eyes-the things moving in the heavens-appeared to them to be full of stones and earth and many other soulless bodies, which dispose the causes of all the universe.

Phaedr. 270 A. All the arts that are great require subtlety and the higher kind of philosophy of nature so such loftiness and complete effectiveness seem to come from this source. This Perikles acquired in addition to being a man of genius; for as the result, I think, of his acquaintance with such a man as Anaxagoras he became imbued with high philosophy, and arrived at the nature of intelligence [GREEK] and its opposite, concerning which Anaxagoras often discoursed, so that he brought to the art of speaking what was advantageous to him.

Phys. i. 4; 187 a 20. And others say that the opposites existing in the one are separated out of it, as Anaximandros says, and as many as say that things are one and many, as Empedokles and Anaxagoras; for these separate other things out of the mixture. . . And Anaxagoras seems to have thought (the elements) infinite because he assumed the common opinion of the physicists to be true, that nothing arises out of non being; for this is why they say, as they do, that all [Page 248] things were together, and he established the fact that such 'arising' was change of form.

Phys. i. 4; 187 a 36. They thought that (what arose) arose necessarily out of things that are and their attributes, and, because the masses were so small, out of what we cannot perceive. Wherefore they say that everything was mixed in everything because they saw everything arising out of everything; and different things appeared and were called different from each other according to what is present in greater number in the mixture of the infinites; for the whole is not purely white or black or sweet or flesh or bone, but the nature of the thing seems to be that of which it has the most.

Phys. iii. 4; 203 a 19. And as many as make the elements infinite, as Anaxagoras and Demokritos, the former out of homoeomeries. . . .

Phys. iii. 5; 205 b 1. Anaxagoras speaks strangely about the permanence of the infinite; for he says that the infinite itself establishes itself-that is, it is in itself; for nothing else surrounds it, so that wherever anything may be, it is there in virtue of its origin.

Phys. iv. 6 ; 213 a 22. Some who try to show that the void does not exist, do not prove this of what men are wont to call a void, but they make the mistake Anaxagoras did and those who attempted to prove it after this manner. For they show that air is something, blowing skins up tight, and showing how strong air is, and shutting it up in clepsydrae.

Phys. viii. 1 ; 250 b 24. For Anaxagoras says that when all things were together and had been at rest for an infinite time, mind introduced motion and caused separation.[3] Phys. viii. 5; 256 b 24. So Anaxagoras is right in [Page 249] saying that mind is not affected by other things and is unmixed, since he makes it the first principle of motion. For thus only, being unmoved, it might move, and being unmixed, it might rule.[4] De caelo i. 3; 270 b 24. Anaxagoras does not use this word [GREEK] rightly, for he uses the word aether instead of fire.

De caelo iii. 2; 301 a 12. Anaxagoras starts to construct the universe out of non-moving bodies.

De caelo iii. 3; 302 a 31. Anaxagoras says the opposite to Empedokles, for he calls the homoeomeries elements (I mean such as flesh and bone and each of those things), and air and fire he calls mixtures of these and of all the other 'seeds;' for each of these things is made of the invisible homoeomeries all heaped together. Wherefore all things arise out of these things; for he calls fire and aether the same. And since there is a peculiar motion of every material body, and some motions are simple and some complex, and the complex motions are those of complex bodies and the simple motions of simple bodies, it is evident that there will be simple bodies. For there are also simple motions. So it is evident what elements are, and why they are.

De caelo iv. 2; 309 a 20. Some of those who deny that there is a void say nothing definite concerning lightness and weight, for instance Anaxagoras and Empedokles.

Gen. corr. i. 1 ; 314 a 11. Others assert that matter more than one, as Empedokles and Leukippos and Anaxagoras, but there is a difference between these. And Anaxagoras even ignores his own word, for he says that he has shown genesis and destruction to be the same as change, but like the others, he says there are many elements. . . Anaxagoras et al. say there [Page 250] are an infinite number of elements. For he regards the homoeomeries as elements, such as bone and flesh and marrow, and other things of which the part [GREEK] has the same name as the whole.

De anima i. 2; 404 a 25. In like manner Anaxagoras says that soul is the moving power, and if any one else has said that mind moved the all, no one said it absolutely as did Demokritos.

De anima i. 2; 404 b 1. Anaxagoras speaks less clearly about these things; for many times he rightly and truly says that mind is the cause, while at other times he says it is soul; for (he says) it is in all animals, both great and small, both honoured and dishonoured. But it is not apparent that what is intelligently called mind is present in all animals alike, nor even in all men.

De anima i.2 ; 405 a 13. Anaxagoras seems to say that soul and mind are different, as we said before, but he treats both as one in nature, except that he regards mind especially as the first principle of all things; for he says that this alone of all things is simple and unmixed and pure. And he assigns both to the same first principle, both knowledge and motion, saying that mind moves the all.[5]

De anima i. 19; 405 b 19. Anaxagoras alone says: that mind does not suffer change, and has nothing in common with any of the other things.

De anima iii. 4 ; 429 a 18. It is necessary then that it be unmixed since it knows [GREEK] all things, as Anaxagoras says, in order that it may rule, that is, that it may know [GREEK].

De part. anim. iv. 10; 687 a 7. Anaxagoras says that man is the most intelligent of animals because he has hands. [Page 251] De plant. i. ; 815 a 16. Anaxagoras said that plants are animals and feel pleasure and pain, inferring this because they shed their leaves and let them grow again.

De plant. i. ; 816 b 26. Anaxagoras said that plants have these (motion and sensation) and breathing.

De plant. i.; 817 a 26. Anaxagoras said that their moisture is from the earth, and on this account he said to Lechineos that the earth is mother of plants, and the sun father.

De X. Z. G. ii.; 976 b 20. Anaxagoras busying himself on this point, was satisfied with saying that the void does not exist, nevertheless he says beings move, though there is no void.

Meta. i. 3; 984 a 11. Anaxagoras of Klazomenac, who preceded him (Empedokles) in point of age and followed him in his works, says that the first principles are infinite in number; for nearly all things being made up of like parts (homoeomeries), as for instance fire and water, he says arise and perish only by composition and separation, and there is no other arising and perishing, but they abide eternal.

Meta. i. 3 ; 984 b 8. Besides these and similar causes, inasmuch as they are not such as to generate the nature of things, they (again compelled, as we said, by the truth itself) sought the first principle which lay nearest. For perhaps neither fire nor earth nor any other such thing should fittingly be or be thought a cause why some things exist and others arise; nor is it well to assign any such matter to its voluntary motion or to chance. Moreover one who said that as mind exists in animals, so it exists in nature as the cause of the universe and of all order, appeared as a sober man in contrast with those before who spoke rashly.

Meta. i. 4; 985 a 18. Anaxagoras uses mind as a device by which to construct the universe, and when he is [Page 252] at a loss for the cause why anything necessarily is, then he drags this in, but in other cases he assigns any other cause rather than mind for what comes into being.

Meta. i. 8; 989 a 30. And if any one were to assume that Anaxagoras said the elements were two, he certainly would assume it according to a principle which that one did not describe distinctly; nevertheless he would follow along a necessary path those who guided him. For though it is strange particularly that he said all things had been mixed together at first, and that they must first have existed unmixed because they came together, and because chance had not in its nature to be mingled with chance; and in addition to this it is strange that he should separate qualities and accidental characteristics from essences (for there is mixture and separation of these), nevertheless if any one should follow him and try to put together what he wanted to say, perhaps he would seem to speak in a very novel manner. For when nothing was separated, clearly it was not possible to say anything true of that essence, I mean to. say that anything was white or black or grey or any other colour, but everything was necessarily colourless; for it might have any of these colours. In like manner it is tasteless, nor according to the same line of argument could it have any other of the like qualities; for it could not have any quality, or quantity, or anything. For then one of what are sometimes called forms would exist for it, and this is impossible when all things are mixed together; for it would have been already separated, and he says that all things are mixed together except mind, and this alone is unmixed and pure. It results from these views that he says the first principles are unity (for this is simple and unmixed), and what is different from unity, such as we suppose the undefined to be before it was defined and partook of any form. So he [Page 253] does not speak rightly or clearly, still he means something like those who spoke later and with greater clearness.

Meta. iii. 5 ; 1009 b 25. And he called to mind the saying of Anaxagoras that just such things as men assume will be real for them.

Meta. iii. 7; 1012 a 26. The thought of Anaxagoras that some things exist between contradictory propositions, so that all things are false; for when they are mixed together, the mixture is neither good nor not-good, so that there is nothing true to be said.[6]

Meta. x. 6; 1063 b 25. According to the position of Herakleitos, or of Anaxagoras, it is not possible to speak the truth.

Ethic. vi. 5; 1141 b 3. Wherefore they say that Thales and Anaxagoras and such wise men are lacking in intelligence, when they see them ignorant in things that are for their own advantage, and they say they know things extraordinary and wonderful and dreadful and divine, but these are of no use, because they do not seek human good.

Ethic. x. 9; 1179 a 13. And Anaxagoras did not seem to regard the rich man nor yet the powerful man as the happy one when he said he would not be surprised if any one appeared strange to the many; for these judge by what is outside, for that is all they can see.

Aet. Plac. i. 3; Dox. 279. Anaxagoras of Klazomenae declared that homoeomeries are the first principles of things. For he thought it most difficult to [Page 254] understand how anything should arise out of not-being, or perish into not-being. Certainly we take simple food of one kind, such as the bread of Demeter, and we drink water; and from this nourishment there are nurtured hair, veins, arteries, sinews, bones, and the other parts. Since these arise we must acknowledge that in the nourishment that is taken are present all realities, and from them everything will grow. And in that nourishment there are parts productive of blood and of sinews and bones and the rest; these are the parts that may be discovered by contemplation. For it is not necessary to perceive everything by sense, how that bread and water give rise to these things, but the parts may be discovered in them by contemplation. From the fact that parts exist in the nourishment like the things that are generated, he called them homoeomeries, and declared that they are the first principles of things; and he called the homoeomeries matter, but the active cause that arranges all things is mind. And he began thus: All things were together and mind arranged and disposed them. So we must assert that he associated an artificer with matter. i. 7; 299. Anaxagoras says that bodies are established according to first principles, and the mind of God arranged them and caused the generations of all things. i. 7 ; 302. The mind that made the universe is God. i. 14; 312. Anaxagoras: The homoeomeries are of many shapes. i. 17 ; 315. Anaxagoras and Demokritos : The elements are mixed by juxtaposition. i. 24 ; 320. (See p. 241. i. 29; 326.) Anaxagoras and the Stoics: Cause is not evident to human reason; for some things happen by necessity, and others by fate, and others by purpose, and others by chance, and others of their own accord. i. 30; 326. Anaxagoras: Origination is at the same time composition and separation, that is, genesis and destruction. [Page 255] Aet. Plac. ii. 1; 327. The universe is one. 11.4; 331. The universe is perishable. ii. 8; 337. Diogenes and Anaxagoras: After the universe arose and the animals were brought forth out of the earth it tipped somehow of its own accord towards its south part, perhaps intentionally, in order that some parts of the universe might be inhabited and others uninhabited according as they are cold, or hot, or temperate. ii. 13; 341. Anaxagoras: The surrounding aether is of a fiery nature, and catching up stones from the earth by the power of its rotation and setting them on fire it has made them into stars. ii. 16; 345. Anaxagoras et al.: All the stars move from east to west. ii. 21; 351. Anaxagoras: The sun is many times as large as the Peloponnesos. ii. 23 ; 352. Anaxagoras: The solstices are due to a repulsion of the air towards the south, for the sun compressed it and by condensation made it strong. ii. 25; 356. Anaxagoras and Demokritos: The moon is a fiery solid body having in itself plains and mountains and valleys. ii. 2,9; 360. Anaxagoras, as Theophrastos says, attributed eclipses to bodies below the moon which sometimes come in front of it.[7] ii. 30; 361. Anaxagoras says that the unevenness of the composition (the surface of the moon) is due to the mixture of earthy matter with cold, since the moon has some high places and some low hollows. And the dark stuff is mingled with the fiery, the result of which is the shadowy appearance; whence it is called a false-shining star.

Aet. Plac. iii. 1; 365. Anaxagoras: The shadow of the earth falls along this part of the heaven (the milky way), when the sun is beneath the earth and does not shed light on all things. iii. 2; 366. Anaxagoras and Demokritos: (Comets etc.) are due to the conjunction of two or more stars, and the combination of their rays. 367. [Page 256] The so-called shooting stars come darting down from the aether like sparks, and so they are immediately extinguished. iii. 3; 368. Anaxagoras: When the hot falls on the cold (that is, aether on air), it produces thunder by the noise it makes, and lightning by the colour on the black of the cloud, and the thunderbolt by the mass and amount of the light, and the typhoon by the more material fire, and the fiery whirlwind by the fire mixed with cloud. iii.4; 371. Anaxagoras: Clouds and snow are formed in somewhat the same manner; and hail is formed when, already cooled by its descent earthwards, it is thrust forth from frozen clouds; and it is made round. iii. 5; 373. Anaxagoras: (The rainbow) is a reflection of the sun's brightness from thick cloud, and it is always set opposite the star which gives rise to the reflection. And in a similar way he accounts for the so-called parhelia, which take place along the Pontos. iii. 15; 379. Anaxagoras: (Earthquakes take place) when the air falls on the thickness of the earth's surface in a sheltered place, and it shakes the surrounding medium and makes it tremble because it is unable to effect a separation. iii. 16; 381. Anaxagoras: When the moisture which was at first gathered in pools was burned all around by the revolution of the sun, and the fresh water was evaporated into saltness and bitterness, the rest (of the sea) remained. Aet. Plac. iv. 1; 385. Anaxagoras: The Nile comes from the snow in Ethiopia which melts in summer and freezes in winter. iv. 3; 387. Anaxagoras et al. : The soul is of the nature of air. iv. 5, 392. The intelligence is gathered in the breast. The soul is imperishable. iv. 9; 396. Anaxagoras et al.: Sensations are deceptive. 397. Sensations arise part by part according to the symmetry of the pores, each particular object of sense corresponding to a particular sense (organ). iv. 19; 409. Anaxagoras: Sound arises when wind falls [Page 257] on solid air, and by the return of the blow which is dealt to the ear; so that what is called an echo takes place.

Aet. Plac. v. 7; 420. Anaxagoras, Parmenides: Males are conceived when seed from the right side enters the right side of the womb, or seed from the left side the left side of the womb; but if its course is changed females are born. v. 19; 430. As Anaxagoras and Euripides say : Nothing of what is born dies, but one thing separated from one part and added to another produces different forms. v. 20; 432. Anaxagoras : All animals have reason that shows itself iii activity, but they do not have a sort of intelligence that receives impressions, which may be called the interpreter of intelligence. v.25; 437. Anaxagoras: Sleep is due to a weariness of the body's energy; for it is an experience of the body, not of the soul; and death is the separation of the soul from the body.

Theophr. Phys. opin. Fr. 4; Dox. 479. Theophrastos says that the teaching of Anaxagoras is much like that of Anaximandros; for Anaxagoras says that in the separation of the infinite, things that are akin come together, and whatever gold there is in the all becomes gold, and whatever earth becomes earth, and in like manner each of the other things, not as though they came into being, but as though they were existing before. And Anaxagoras postulated intelligence [GREEK] as the cause of motion and of coming in to being, and when this caused separation worlds were produced and other objects sprang forth. lie might seem, he says, to make the material causes of things taking place thus infinite, but the cause of motion and of coming in to being one. But if one were to assume that the mixture of all things were one nature undefined in form and in amount, which he seems to mean, it follows that he [Page 258] speaks of two first principles, the nature of the infinite and intelligence, so that he appears to treat all the material elements in much the same manner as Anaximandros.

Phys. op. Fr. 19; Dox. 493. See Aet. ii. 29; Dox. 360, translated above, p.255.

Phys. opin. Fr. 23 ; Dox. 495. And the third opinion about the sea is that the water which filters and strains through the earth becomes salt because the earth has in it; and they point out as a proof of this that salt and saltpetre are dug up out of the earth, and there are bitter flavours at many places in the Anaxagoras and Metrodoros came to be of this opinion. Theophr. de sens. 27; Dox. 507. Anaxagoras held that sensation takes place by opposite qualities; for like is not affected by like. And he attempts to enumerate things one by one. For seeing is a reflection in the pupil, and objects are not reflected in the like, but in the opposite. And for many creatures there is a difference of colour in the daytime, and for others at night, so that at that time they are sharpsighted. But in general the night is more of the same colour as the eyes. And the reflection takes place in the daytime, since light is the cause of reflection ; but that colour which prevails the more is reflected in its opposite. In the same manner both touch and taste discern; for what is equally warm or equally cold does not produce warm or cold when it approaches its like, nor yet do men recognise sweet or bitter by these qualities in themselves, but they perceive the cold by the warm, the drinkable water by the salt, the sweet by the bitter, according as each quality is absent ; for all things are existing in us. So also smell and hearing take place, the one in connection with breathing, the other by the penetration of sound into [Page 259] the brain; for the surrounding bone against which the sound strikes is hollow. And every sensation is attended with pain, which would seem to follow from the fundamental thesis; for every unlike thing by touching produces distress. And this is evident both in the duration and in the excessive intensity of the sensations. For both bright colours and very loud sounds occasion pain, and men are not able to bear them for any long time. And the larger animals have the more acute sensations, for sensation is simply a matter of size. For animals that have large, pure, and bright eyes see large things afar off, but of those that have small eyes the opposite is true. And the same holds true of hearing. For large ears hear large sounds afar off, smaller ones escape their notice, and small ears hear small sounds near at hand. And the same is true of smell; for the thin air has the stronger odour, since warm and rarefied air has an odour. And when a large animal breathes, it draws in the thick with the rarefied, but the small animal only the rarefied, so that large animals have a better sense of smell. For an odour near at hand is stronger than one far off, because that is thicker, and what is scattered is weakened. It comes about to this, large animals do not perceive the thin air, and small animals do not perceive the thick air.

Cic. de Nat. Deor. i. 11; Dox. 532. Whence Anaxagoras, who was a pupil of Anaximenes, first taught that the separation and character of all things were determined and arranged by the power and reason of infinite mind; but in this he fails to see that no motion can be connected with and contiguous to inflinite sensation, and that no sensation at all can exist, by which nature as a whole can feel a shock. Wherefore if he meant that mind is as it were sonic sort of living being, there will be something inside of it from which that living being [Page 260] is determined. But what could be inside of mind? So the living being would be joined with an external body. But since this is not satisfactory, and mind is 'open and simple,' joined with nothing by means of which it can feel, he seems to go beyond the scope of our intelligence.

Hipp. Phil. 8 ; Dox. 561. After him came Anaxagoras of Klazomenae, son of Hegesiboulos. He said that the first principle of the all is mind and matter, mind the active first principle, and matter the passive. For when all things were together, mind entered and disposed them. The material first principles are infinite, and the smaller ones of these he calls infinite. And all things partake of motion when they are moved by mind and like things come together. And objects in the heavens have been ordered by their circular motion. The dense and the moist and the dark and the cold and all heavy things come together into the midst, and the earth consists of these when they are solidified; but the opposite to these, the warm, the bright, the dry, and the light move out beyond the aether. The earth is flat in form, and keeps its place in the heavens because of its size and because there is no void; and on this account the air by its strength holds up the earth, which rides on the air. And the sea arose from the moisture on the earth, both of the waters which have fallen after being evaporated, and of the rivers that flow down into it.[8] And the rivers get their substance from the clouds and from the waters that are in the earth. For the earth is hollow and has water in the hollow places. And the Nile increases in summer because waters flow down into it from snows at the north.[9] Sun and moon and all the stars are fiery stones that [Page 261] are borne about by the revolution of the aether. And sun and moon and certain other bodies moving with them, but invisible to us, are below the stars. Men do not feel the warmth of the stars, because they are so far away from the earth; and they are not warm in the way that the sun is, because they are in a colder region. The moon is below the sun and nearer us. The sun is larger than the Peloponnesos. The moon does not have its own light, but light from the sun. The revolution of the stars takes them beneath the earth. The moon is eclipsed when the earth goes in front of it, and sometimes when the bodies beneath the moon go in front of it; and the sun is eclipsed when the new moon goes in front of it. And the solstices are occasioned because the sun and the moon are thrust aside by the air. And the moon changes its course frequently because it is not able to master the cold. He first determined the matter of the moon's phases. He said the moon is made of earth and has plains and valleys in it. The milky way is a reflection of the light of the stars which do not get their light from the sun. The stars which move across the heavens, darting down like sparks, are due to the motion of the sphere.

And winds arise when the air is rarefied by the sun, and when objects are set on fire and moving towards the sphere are borne away. Thunders and lightnings arise from heat striking the clouds. Earthquakes arise from the air above striking that which is beneath the earth; for when this is set in motion, the earth which rides on it is tossed about by it. And animals arose in the first place from moisture, and afterwards one from another; and males arise when the seed that is separated from the right side becomes attached to the right side of the womb, and females when the opposite is the case. He was in his prime in the first year of the [Page 262] eighty-eighth Olympiad, at the time when it is said Plato was born. They say that he became endowed with knowledge of the future.

Herm. I. G. P.6; Dox. 652. Anaxagora takes me aside and instructs me as follows:-Mind is the first principle of all things, and it is the cause and master of all, and it provides arrangement for what is disarranged, and separation for what has been mixed, and an orderly universe for what was disorderly.

Footnotes

[1] I.e.things are called after the element or elements (homoeomeries) which predominate in their make-up.

Leucippus was the founder of Atomism. We know next to nothing about his life, and his book appears to have been incorporated in the collected works of Democritus. No writer subsequent to Theophrastos seems to have been able to distinguish his teaching from that of his more famous disciple. Indeed his very existence has been denied, though on wholly insufficient grounds.

Aristotle gives a clear and intelligible account of the way Leucippus' theory arose. It originated from Parmenides' denial of the void, from which the impossibility of multiplicity and motion had been deduced. Leucippus supposed himself to have discovered a theory which would avoid this consequence. He admitted that there could be no motion if there was no void, and he inferred that it was wrong to identify the void with the non-existent. Leucippus was the first philosopher to affirm, with a full consciousness of what he was doing, the existence of empty space. The Pythagorean void had been more or less identified with 'air', but the void of Leucippus was really a vacuum.

Besides space there was body, and to this Leucippus ascribed all the characteristics of Parmenides notion of the real. The assumption of empty space, however, made it possible to affirm that there was an infinite number of such reals, invisible because of their smallness, but each possessing all the marks of the Parmenidean One, and in particular each indivisible like it. These moved in the empty space, and their combinations can give rise to the things we perceive with the senses. Pluralism was at least stated in a logical and coherent way. Democritus compared the motions of the atoms of the soul to that of the particles in the sunbeam which dart hither and thither in all directions even when there is no wind, and we may fairly assume that he regarded the original motion of the other atoms in much the same way.

The atoms are not mathematically indivisible like the Pythagorean monads, but they are physically indivisible because there is no empty space in them. Theoretically, then, there is no reason why an atom should not be as large as a world. Such an atom would be much the same thing as the Sphere of Parmenides, were it not for the empty space outside it and the plurality of worlds. As a matter of fact, however, all atoms are invisible. That does not mean, of course, that they are all the same size; for there is room for an infinite variety of sizes below the limit of the minimum visible. Leucippus explained the phenomenon of weight from the size of the atoms and their combustions, but he did not regard weight itself as a primary property of bodies. Aristotle distinctly says that none of his predecessors had said anything of absolute weight and lightness, but only of relative weight and lightness, and Epicurus was the first to ascribe weight to atoms. Weight for the earlier atomists is only a secondary phenomenon arising, in a manner to be explained, from excess of magnitude. It will be observed that in this respect the early atomists were far more scientific than Epicurus and even than Aristotle. The conception of absolute weight has no place in science, and it is really one of the most striking illustrations of the true scientific instinct of the Greek philosophers that no one before Aristotle ever made use of it, and Plato expressly rejected it.

The first effect of the motion of the atoms is that the larger atoms are retarded, not because they are 'heavy', but because they are more exposed to impact than the smaller. In particular, atoms of an irregular shape become entangled with one another and form groups of atoms, which are still more exposed to impact and consequent retardation. The smallest and roundest atoms, on the other hand, preserve their original motions best, and these are the atoms of which fire is composed. In an infinite void in which an infinite number of atoms of countless shapes and sizes are constantly impinging upon one another in all directions, there will be an infinite number of places where a vortex motion is set up by their impact. when this happens, we have the beginning of a world. It is not correct to ascribe this to chance, as later writers do. It follows necessarily from the presuppositions of the system. The solitary fragment of Leucippus we possess is to the effect that 'Naught happens for nothing, but all things from a ground (logos) and of necessity'.

Democritus of Abdera is best known for his atomic theory but he was also an excellent geometer. Very little is known of his life but we know that Leucippus was his teacher.

Democritus certainly visited Athens when he was a young man, principally to visit Anaxagoras, but Democritus complained how little he was known there. He said, according to Diogenes Laertius writing in the second century AD [5]:-

Democritus was disappointed by his trip to Athens because Anaxagoras, then an old man, had refused to see him.

How different he would find the trip today, where the main approach to the city from the northeast runs past the impressive "Democritus Nuclear Research Laboratory".

Certainly Democritus made many journeys other than the one to Athens. Russell in [9] writes:-

He travelled widely in southern and eastern lands in search of knowledge, he perhaps spent a considerable time in Egypt, and he certainly visited Persia. He then returned to Abdera, where he remained.

Democritus himself wrote (but some historians dispute that the quote is authentic) (see [5]):-

Of all my contemporaries I have covered the most ground in my travels, making the most exhaustive inquiries the while; I have seen the most climates and countries and listened to the greatest number of learned men.

His travels certainly took him to Egypt and Persia, as Russell suggests, but he almost certainly also travelled to Babylon, and some claim he travelled to India and Ethiopia. Certainly he was a man of great learning. As Heath writes in [7]:-

... there was no subject to which he did not notably contribute, from mathematics and physics on the one hand to ethics and poetics on the other; he even went by the name of 'wisdom'.

Although little is known of his life, quite a lot is known of his physics and philosophy. There are two main sources for our knowledge of his of physical and philosophical theories. Firstly Aristotle discusses Democritus's ideas thoroughly because he strongly disagreed with his ideas of atomism. The second source is in the work of Epicurus but, in contrast to Aristotle, Epicurus is a strong believer in Democritus's atomic theory. This work of Epicurus is preserved by Diogenes Laertius in his second century AD book [5].

Certainly Democritus was not the first to propose an atomic theory. His teacher Leucippus had proposed an atomic system, as had Anaxagoras of Clazomenae. In fact traces of an atomic theory go back further than this, perhaps to the Pythagorean notion of the regular solids playing a fundamental role in the makeup of the universe. However Democritus produced a much more elaborate and systematic view of the physical world than had any of his predecessors. His view is summarised in [2]:-

Democritus asserted that space, or the Void, had an equal right with reality, or Being, to be considered existent. He conceived of the Void as a vacuum, an infinite space in which moved an infinite number of atoms that made up Being (i.e. the physical world). These atoms are eternal and invisible; absolutely small, so small that their size cannot be diminished (hence the name atomon, or "indivisible"); absolutely full and incompressible, as they are without pores and entirely fill the space they occupy; and homogeneous, differing only in shape, arrangement, position, and magnitude.

With this as a basis to the physical world, Democritus could explain all changes in the world as changes in motion of the atoms, or changes in the way that they were packed together. This was a remarkable theory which attempted to explain the whole of physics based on a small number of ideas and also brought mathematics into a fundamental physical role since the whole of the structure proposed by Democritus was quantitative and subject to mathematical laws. Another fundamental idea in Democritus's theory is that nature behaves like a machine, it is nothing more than a highly complex mechanism.

There are then questions for Democritus to answer. Where do qualities such as warmth, colour, and taste fit into the atomic theory? To Democritus atoms differ only in quantity, and all qualitative differences are only apparent and result from impressions of an observer caused by differing configurations of atoms. The properties of warmth, colour, taste are only by convention - the only things that actually exist are atoms and the Void.

Democritus's philosophy contains an early form of the conservation of energy. In his theory atoms are eternal and so is motion. Democritus explained the origin of the universe through atoms moving randomly and colliding to form larger bodies and worlds. There was no place in his theory for divine intervention. Instead he postulated a world which had always existed, and would always exist, and was filled with atoms moving randomly. Vortex motions occurred due to collisions of the atoms and in resulting vortex motion created differentiation of the atoms into different levels due only to their differing mass. This was not a world which came about through the design or purpose of some supernatural being, but rather it was a world which came about through necessity, that is from the nature of the atoms themselves.

Democritus built an ethical theory on top of his atomist philosophy. His system was purely deterministic so he could not admit freedom of choice to individuals. To Democritus freedom of choice was an illusion since we are unaware of all the causes for a decision. Democritus believed that [3]:-

... the soul will either be disturbed, so that its motion affects the body in a violent way, or it will be at rest in which case it regulates thoughts and actions harmoniously. Freedom from disturbance is the condition that causes human happiness, and this is the ethical goal.

Democritus describes the ultimate good, which he identifies with cheerfulness, as:-

... a state in which the soul lives peacefully and tranquilly, undisturbed by fear or superstition or any other feeling.

He wanted to remove the belief in gods which were, he believed, only introduced to explain phenomena for which no scientific explanation was then available.

Very little is known for certainty about Democritus's contributions to mathematics. As stated in the Oxford Classical Dictionary :-

Little is known (although much is written) about the mathematics of Democritus.

We do know that Democritus wrote many mathematical works. Diogenes Laertius (see [5]) lists his works and gives Thrasyllus as the source of this information. He wrote On numbers, On geometry, On tangencies, On mappings, On irrationals but none of these works survive. However we do know a little from other references. Heath [7] writes:-

In the Method of Archimedes, happily discovered in 1906, we are told that Democritus was the first to state the important propositions that the volume of a cone is one third of that of a cylinder having the same base and equal height, and that the volume of a pyramid is one third of that of a prism having the same base and equal height; that is to say, Democritus enunciated these propositions some fifty years or more before they were first scientifically proved by Eudoxus.

There is another intriguing piece of information about Democritus which is given by Plutarch in his Common notions against the Stoics where he reports on a dilemma proposed by Democritus as reported by the Stoic Chrysippus (see [7], [10] or [11]).

If a cone were cut by a plane parallel to the base [by which he means a plane indefinitely close to the base], what must we think of the surfaces forming the sections? Are they equal or unequal? For, if they are unequal, they will make the cone irregular as having many indentations, like steps, and unevennesses; but, if they are equal, the sections will be equal, and the cone will appear to have the property of the cylinder and to be made up of equal, not unequal, circles, which is very absurd.

There are important ideas in this dilemma. Firstly notice, as Heath points out in [7], that Democritus has the idea of a solid being the sum of infinitely many parallel planes and he may have used this idea to find the volumes of the cone and pyramid as reported by Archimedes. This idea of Democritus may have led Archimedes later to apply the same idea to great effect. This idea would eventually lead to theories of integration.

There is much discussion in [7], [8], [10] and [11] as to whether Democritus distinguished between the geometrical continuum and the physical discrete of his atomic system. Heath points out that if Democritus carried over his atomic theory to geometrical lines then there is no dilemma for him since his cone is indeed stepped with atom sized steps. Heath certainly believed that to Democritus lines were infinitely divisible. Others, see for example [10], have come to the opposite conclusion, believing that Democritus made contributions to problems of applied mathematics but, because of his atomic theory, he could not deal with the infinitesimal questions arising.

Hippocrates of Chios

Born: about 470 BC in Chios (now Khios), Greece
Died: about 410 BC

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Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating the cube. Little is known of his life but he is reported to have been an excellent geometer who, in other respects, was stupid and lacking in sense. Some claim that he was defrauded of a large sum of money because of his naiveté. Iamblichus [4] writes:-

One of the Pythagoreans [Hippocrates] lost his property, and when this misfortune befell him he was allowed to make money by teaching geometry.

One version of the story is that [Hippocrates] was a merchant, but lost all his property through being captured by a pirate vessel. He then came to Athens to persecute the offenders and, during a long stay, attended lectures, finally attaining such proficiency in geometry that he tried to square the circle.

... he allowed himself to be defrauded of a large sum by custom-house officers at Byzantium, thereby proving, in Aristotle's opinion, that, though a good geometer, he was stupid and incompetent in the business of ordinary life.

The suggestion is that this 'long stay' in Athens was between about 450 BC and 430 BC.

In his attempts to square the circle, Hippocrates was able to find the areas of lunes, certain crescent-shaped figures, using his theorem that the ratio of the areas of two circles is the same as the ratio of the squares of their radii. We describe this impressive achievement more fully below.

Hippocrates also showed that a cube can be doubled if two mean proportionals can be determined between a number and its double. This had a major influence on attempts to duplicate the cube, all efforts after this being directed towards the mean proportionals problem.

He was the first to write an Elements of Geometry and although his work is now lost it must have contained much of what Euclid later included in Books 1 and 2 of the Elements. Proclus, the last major Greek philosopher, who lived around 450 AD wrote:-

Hippocrates of Chios, the discoverer of the quadrature of the lune, ... was the first of whom it is recorded that he actually compiled "Elements".

Hippocrates' book also included geometrical solutions to quadratic equations and included early methods of integration.

Eudemus of Rhodes, who was a pupil of Aristotle, wrote History of Geometry in which he described the contribution of Hippocrates on lunes. This work has not survived but Simplicius of Cilicia, writing in around 530, had access to Eudemus's work and he quoted the passage about the lunes of Hippocrates 'word for word except for a few additions' taken from Euclid's Elements to make the description clearer.

We will first quote part of the passage of Eudemus about the lunes of Hippocrates, following the historians of mathematics who have disentangled the additions from Euclid's Elements which Simplicius added. See [6] both for the translation which we give and for a discussion of which parts are due to Eudemus:-

The quadratures of lunes, which were considered to belong to an uncommon class of propositions on account of the close relation of lunes to the circle, were first investigated by Hippocrates, and his exposition was thought to be correct; we will therefore deal with them at length and describe them. He started with, and laid down as the first of the theorems useful for the purpose, the proposition that similar segments of circles have the same ratio to one another as the squares on their bases. And this he proved by first showing that the squares on the diameters have the same ratio as the circles.

Before continuing with the quote we should note that Hippocrates is trying to 'square a lune' by which he means to construct a square equal in area to the lune. This is precisely what the problem of 'squaring the circle' means, namely to construct a square whose area is equal to the area of the circle. Again following Heath's translation in [6]:-

After proving this, he proceeded to show in what way it was possible to square a lune the outer circumference of which is that of a semicircle. This he affected by circumscribing a semicircle about an isosceles right-angled triangle and a segment of a circle similar to those cut off by the sides. Then, since the segment about the base is equal to the sum of those about the sides, it follows that, when the part of the triangle above the segment about the base is added to both alike, the lune will be equal to the triangle. Therefore the lune, having been proved equal to the triangle, can be squared.

ABCD is a square and O is its centre. The two circles in the diagram are the circle with centre O through A, B, C and D, and the circle with centre D through A and C.

Notice first that the segment marked 1 on AB subtends a right angle at the centre of the circle (the angle AOB) while the segment 2 on AC also subtends a right angle at the centre (the angle ADC).

Therefore the segment 1 on AB and the segment 2 on AC are similar. Now
segment 1/segment 2 = AB²/AC² = ¹/₂ since AB² + BC² = AC² by Pythagoras's theorem, and AB = BC so AC² = 2AB².

Now since segment 2 is twice segment 1, the segment 2 is equal to the sum of the two segments marked 1.

Then Hippocrates argues that the semicircle ABC with the two segments 1 removed is the triangle ABC which can be squared (it was well known how to construct a square equal to a triangle).

However, if we subtract the segment 2 from the semicircle ABC we get the lune shown in the second diagram. Thus Hippocrates has proved that the lune can be squared.

However, Hippocrates went further than this in studying lunes. The proof we have examined in detail is one where the outer circumference of the lune is the arc of a semicircle. He also studied the cases where the outer arc was less than that of a semicircle and also the case where the outer arc was greater than a semicircle, showing in each case that the lune could be squared. This was a remarkable achievement and a major step in attempts to square the circle. As Heath writes in [6]:-

... he wished to show that, if circles could not be squared by these methods, they could be employed to find the area of some figures bounded by arcs of circles, namely certain lunes, and even of the sum of a certain circle and a certain lune.

There is one further remarkable achievement which historians of mathematics believe that Hippocrates achieved, although we do not have a direct proof since his works have not survived. In Hippocrates' study of lunes, as described by Eudemus, he uses the theorem that circles are to one another as the squares on their diameters. This theorem is proved by Euclid in the Elements and it is proved there by the method of exhaustion due to Eudoxus. However, Eudoxus was born within a few years of the death of Hippocrates, and so there follows the intriguing question of how Hippocrates proved this theorem. Since Eudemus seems entirely satisfied that Hippocrates does indeed have a correct proof, it seems almost certain from this circumstantial evidence that we can deduce that Hippocrates himself developed at least a variant of the method of exhaustion.

THALES OF MILETUS

ANAXIMANDER

Alcmaeon

Life and Works

1.1 Medical Writer or Philosopher?

1.2 Was Alcmaeon a Pythagorean?

1.3 Date

1.4 Alcmaeon's Book and the Evidence for Its Contents

2. Epistemology and Psychology

2.1 The Limits of Knowledge

2.2 Understanding and Empiricism

2.3 Did Alcmaeon Practice Dissection?

2.4 Sense Preception

2.5 The Immortality of the Soul

3. Medical Doctrines

3.1 Health and Disease

3.2 Sleep, Embryology, and the Use of Analogy

4. Cosmology

4.1 Astronomy

4.2 Opposites

5. Importance and Influence

Bibliography

Texts and Commentaries

General Bibliography

Fairbanks's Introduction

Translation of the Fragments: Book I

Translation of the Fragments: Book II

Translation of the Fragments: Book III

Translation of the Fragments: On Purifications

Passages from Plato relating to Empedokles

Passages in Aristotle referring to Empedokles

Passages in Diels' 'Doxographi Graeci' relating to Empedokles

Fairbanks's Introduction

The Fragments of Anaxagoras

Ancient Authors' Commentaries on Anaxagoras

Literature:--Shaubach, Anax. Claz. Frag. Lips. 1827; W. Schorn, Anax. Claz. et Diog. Apoll. Frag. Bonn 1829; Panzerbieter, De frag. Anax. ord. Meining. 1936; Fr. Breier, Die Philosophie des Anax. nach Arist. Berl. 1840. Cf. Diels, Hermes xiii. 4.

Footnotes

Hippocrates of Chios

Born: about 470 BC in Chios (now Khios), Greece
Died: about 410 BC

THALES OF MILETUS

ANAXIMANDER

Alcmaeon

Life and Works

1.1 Medical Writer or Philosopher?

1.2 Was Alcmaeon a Pythagorean?

1.3 Date

1.4 Alcmaeon's Book and the Evidence for Its Contents

2. Epistemology and Psychology

2.1 The Limits of Knowledge

2.2 Understanding and Empiricism

2.3 Did Alcmaeon Practice Dissection?

2.4 Sense Preception

2.5 The Immortality of the Soul

3. Medical Doctrines

3.1 Health and Disease

3.2 Sleep, Embryology, and the Use of Analogy

4. Cosmology

4.1 Astronomy

4.2 Opposites

5. Importance and Influence

Bibliography

Texts and Commentaries

General Bibliography

Fairbanks's Introduction

Translation of the Fragments: Book I

Translation of the Fragments: Book II

Translation of the Fragments: Book III

Translation of the Fragments: On Purifications

Passages from Plato relating to Empedokles

Passages in Aristotle referring to Empedokles

Passages in Diels' 'Doxographi Graeci' relating to Empedokles

Fairbanks's Introduction

The Fragments of Anaxagoras

Ancient Authors' Commentaries on Anaxagoras

Literature:--Shaubach, Anax. Claz. Frag. Lips. 1827; W. Schorn, Anax. Claz. et Diog. Apoll. Frag. Bonn 1829; Panzerbieter, De frag. Anax. ord. Meining. 1936; Fr. Breier, Die Philosophie des Anax. nach Arist. Berl. 1840. Cf. Diels, Hermes xiii. 4.

Footnotes

Hippocrates of Chios

Born: about 470 BC in Chios (now Khios), Greece Died: about 410 BC

Born: about 470 BC in Chios (now Khios), Greece
Died: about 410 BC